> CoreThms(70,16,1,1); Let X_n be the random variable "size of an (n,n+1)-core partition into distinct parts," and F(n) be the nth Fibonacci number. Theorem 0: The number of (n,n+1) core partitions into distinct parts Is F(n+1). Theorem 1: E[X_n]= (1/50)*(5*n^2*F(n+1)+7*n*F(n+1)-6*F(n)*n-6*F(n))/F(n+1) which is asymptotic to (1/50)*(5*n^2*r+7*n*r-6*n-6)/r where r is the Golden ratio. Theorem 2: Var(X_n)= (1/1875)*(10*n^3*F(n+1)^2+20*F(n+1)*F(n)*n^3+57*n^2*F(n+1)^2+33*F(n+1)*F(n)*n^2-27*F(n)^2*n^2+65*n*F(n+1)^2-32*F(n+1)*F(n)*n-54*F(n)^2*n-45*F(n)*F(n+1)-27*F(n)^2)/F(n+1)^2 which is asymptotic to (1/1875)*(10*n^3*r^2+20*n^3*r+57*n^2*r^2+33*n^2*r+65*n*r^2-27*n^2-32*n*r-54*n-45*r-27)/r^2 Thus, X_n is concentrated about the mean. Theorem, 3 Central moment, 3, of X_n is -(3/31250)*(65*n^4*F(n+1)^3-40*F(n+1)^2*F(n)*n^4-40*F(n+1)*F(n)^2*n^4+222*n^3*F(n+1)^3-218*F(n+1)^2*F(n)*n^3-106*F(n+1)*F(n)^2*n^3+36*F(n)^3*n^3-65*n^2*F(n+1)^3-338*F(n+1)^2*F(n)*n^2-2*F(n+1)*F(n)^2*n^2+108*F(n)^3*n^2-390*n*F(n+1)^3+110*F(n+1)^2*F(n)*n+154*F(n+1)*F(n)^2*n+108*F(n)^3*n+270*F(n)*F(n+1)^2+90*F(n+1)*F(n)^2+36*F(n)^3)/F(n+1)^3 which is asymptotic to -(3/31250)*(65*n^4*r^3-40*n^4*r^2+222*n^3*r^3-40*n^4*r-218*n^3*r^2-65*n^2*r^3-106*n^3*r-338*n^2*r^2-390*n*r^3+36*n^3-2*n^2*r+110*n*r^2+108*n^2+154*n*r+270*r^2+108*n+90*r+36)/r^3 The limit of the standardized moment is, 0 Theorem, 4 Central moment, 4, of X_n is (1/1171875)*(-729*F(n)^4-2430*F(n+1)*F(n)^3+500*n^6*F(n+1)^4+2610*n^5*F(n+1)^4-7474*n^4*F(n+1)^4-729*F(n)^4*n^4-44660*n^3*F(n+1)^4-2916*F(n)^4*n^3+28955*n^2*F(n+1)^4-4374*F(n)^4*n^2+133025*n*F(n+1)^4-2916*F(n)^4*n-48825*F(n)*F(n+1)^3-14580*F(n+1)^2*F(n)^2-4104*F(n+1)*F(n)^3*n^2-54080*F(n+1)^3*F(n)*n-24030*F(n+1)^2*F(n)^2*n-6588*F(n+1)*F(n)^3*n-240*F(n+1)^3*F(n)*n^5+1620*F(n+1)^2*F(n)^2*n^5+1080*F(n+1)*F(n)^3*n^5+1203*F(n+1)^3*F(n)*n^4+9774*F(n+1)^2*F(n)^2*n^4+3942*F(n+1)*F(n)^3*n^4+8858*F(n+1)^3*F(n)*n^3+19818*F(n+1)^2*F(n)^2*n^3+2916*F(n+1)*F(n)^3*n^3+2160*F(n+1)^3*F(n)*n^2+2214*F(n+1)^2*F(n)^2*n^2)/F(n+1)^4 which is asymptotic to (1/1171875)*(500*n^6*r^4+2610*n^5*r^4-240*n^5*r^3-7474*n^4*r^4+1620*n^5*r^2+1203*n^4*r^3-44660*n^3*r^4+1080*n^5*r+9774*n^4*r^2+8858*n^3*r^3+28955*n^2*r^4+3942*n^4*r+19818*n^3*r^2+2160*n^2*r^3+133025*n*r^4-729*n^4+2916*n^3*r+2214*n^2*r^2-54080*n*r^3-2916*n^3-4104*n^2*r-24030*n*r^2-48825*r^3-4374*n^2-6588*n*r-14580*r^2-2916*n-2430*r-729)/r^4 The limit of the standardized moment is, 3 Theorem, 5 Central moment, 5, of X_n is -(1/19531250)*(5000*F(n+1)^4*F(n)*n^7+23450*F(n+1)^4*F(n)*n^6-15150*F(n+1)^3*F(n)^2*n^6-7200*F(n+1)^2*F(n)^3*n^6-3600*F(n+1)*F(n)^4*n^6-131230*F(n+1)^4*F(n)*n^5-104670*F(n+1)^3*F(n)^2*n^5-49140*F(n+1)^2*F(n)^3*n^5-16740*F(n+1)*F(n)^4*n^5-764130*F(n+1)^4*F(n)*n^4-220490*F(n+1)^3*F(n)^2*n^4-124020*F(n+1)^2*F(n)^3*n^4-22860*F(n+1)*F(n)^4*n^4-365900*F(n+1)^4*F(n)*n^3-29720*F(n+1)^3*F(n)^2*n^3-76320*F(n+1)^2*F(n)^3*n^3+3960*F(n+1)*F(n)^4*n^3+2261050*F(n+1)^4*F(n)*n^2+747350*F(n+1)^3*F(n)^2*n^2+131760*F(n+1)^2*F(n)^3*n^2+35640*F(n+1)*F(n)^4*n^2+3199150*F(n+1)^4*F(n)*n+1134350*F(n+1)^3*F(n)^2*n+198900*F(n+1)^2*F(n)^3*n+30060*F(n+1)*F(n)^4*n+1944*F(n)^5+2500*n^7*F(n+1)^5+13900*n^6*F(n+1)^5-50108*n^5*F(n+1)^5+1944*F(n)^5*n^5+333725*n^4*F(n+1)^5+9720*F(n)^5*n^4+2550550*n^3*F(n+1)^5+19440*F(n)^5*n^3-1481625*n^2*F(n+1)^5+19440*F(n)^5*n^2-9026550*n*F(n+1)^5+9720*F(n)^5*n+1186650*F(n)*F(n+1)^4+488250*F(n+1)^3*F(n)^2+72900*F(n+1)^2*F(n)^3+8100*F(n+1)*F(n)^4)/F(n+1)^5 which is asymptotic to -(1/19531250)*(2500*n^7*r^5+5000*n^7*r^4+13900*n^6*r^5+23450*n^6*r^4-50108*n^5*r^5-15150*n^6*r^3-131230*n^5*r^4+333725*n^4*r^5-7200*n^6*r^2-104670*n^5*r^3-764130*n^4*r^4+2550550*n^3*r^5-3600*n^6*r-49140*n^5*r^2-220490*n^4*r^3-365900*n^3*r^4-1481625*n^2*r^5-16740*n^5*r-124020*n^4*r^2-29720*n^3*r^3+2261050*n^2*r^4-9026550*n*r^5+1944*n^5-22860*n^4*r-76320*n^3*r^2+747350*n^2*r^3+3199150*n*r^4+9720*n^4+3960*n^3*r+131760*n^2*r^2+1134350*n*r^3+1186650*r^4+19440*n^3+35640*n^2*r+198900*n*r^2+488250*r^3+19440*n^2+30060*n*r+72900*r^2+9720*n+8100*r+1944)/r^5 The limit of the standardized moment is, 0 Theorem, 6 Central moment, 6, of X_n is (1/6152343750)*(70000*n^9*F(n+1)^6+3000375*n^8*F(n+1)^6+13429860*n^7*F(n+1)^6-38921316*n^6*F(n+1)^6-91854*F(n)^6*n^6-120407910*n^5*F(n+1)^6-551124*F(n)^6*n^5-287293965*n^4*F(n+1)^6-1377810*F(n)^6*n^4-3099878950*n^3*F(n+1)^6-1837080*F(n)^6*n^3+2028516420*n^2*F(n+1)^6-1377810*F(n)^6*n^2+15502893270*n*F(n+1)^6-551124*F(n)^6*n+2095161390*F(n)*F(n+1)^5-269132220*F(n+1)^4*F(n)^2-55367550*F(n+1)^3*F(n)^3-5511240*F(n+1)^2*F(n)^4-459270*F(n+1)*F(n)^5+140000*F(n+1)^5*F(n)*n^9-441000*F(n+1)^5*F(n)*n^8-1701000*F(n+1)^4*F(n)^2*n^8-23687700*F(n+1)^5*F(n)*n^7-10546200*F(n+1)^4*F(n)^2*n^7+2381400*F(n+1)^3*F(n)^3*n^7+510300*F(n+1)^2*F(n)^4*n^7+204120*F(n+1)*F(n)^5*n^7-89709732*F(n+1)^5*F(n)*n^6+26433540*F(n+1)^4*F(n)^2*n^6+17843490*F(n+1)^3*F(n)^3*n^6+3929310*F(n+1)^2*F(n)^4*n^6+1153278*F(n+1)*F(n)^5*n^6+383100018*F(n+1)^5*F(n)*n^5+267703380*F(n+1)^4*F(n)^2*n^5+44997120*F(n+1)^3*F(n)^3*n^5+11889990*F(n+1)^2*F(n)^4*n^5+2245320*F(n+1)*F(n)^5*n^5+2127249180*F(n+1)^5*F(n)*n^4+333220230*F(n+1)^4*F(n)^2*n^4+29863890*F(n+1)^3*F(n)^3*n^4+12961620*F(n+1)^2*F(n)^4*n^4+1071630*F(n+1)*F(n)^5*n^4-478513070*F(n+1)^5*F(n)*n^3-595695870*F(n+1)^4*F(n)^2*n^3-93044700*F(n+1)^3*F(n)^3*n^3-6327720*F(n+1)^2*F(n)^4*n^3-2245320*F(n+1)*F(n)^5*n^3-9395630370*F(n+1)^5*F(n)*n^2-1572909030*F(n+1)^4*F(n)^2*n^2-225989190*F(n+1)^3*F(n)^3*n^2-26076330*F(n+1)^2*F(n)^4*n^2-3725190*F(n+1)*F(n)^5*n^2-5144409780*F(n+1)^5*F(n)*n-1145549790*F(n+1)^4*F(n)^2*n-187983180*F(n+1)^3*F(n)^3*n-20769210*F(n+1)^2*F(n)^4*n-2163672*F(n+1)*F(n)^5*n-91854*F(n)^6)/F(n+1)^6 which is asymptotic to (1/6152343750)*(70000*n^9*r^6+140000*n^9*r^5+3000375*n^8*r^6-441000*n^8*r^5+13429860*n^7*r^6-1701000*n^8*r^4-23687700*n^7*r^5-38921316*n^6*r^6-10546200*n^7*r^4-89709732*n^6*r^5-120407910*n^5*r^6+2381400*n^7*r^3+26433540*n^6*r^4+383100018*n^5*r^5-287293965*n^4*r^6+510300*n^7*r^2+17843490*n^6*r^3+267703380*n^5*r^4+2127249180*n^4*r^5-3099878950*n^3*r^6+204120*n^7*r+3929310*n^6*r^2+44997120*n^5*r^3+333220230*n^4*r^4-478513070*n^3*r^5+2028516420*n^2*r^6+1153278*n^6*r+11889990*n^5*r^2+29863890*n^4*r^3-595695870*n^3*r^4-9395630370*n^2*r^5+15502893270*n*r^6-91854*n^6+2245320*n^5*r+12961620*n^4*r^2-93044700*n^3*r^3-1572909030*n^2*r^4-5144409780*n*r^5-551124*n^5+1071630*n^4*r-6327720*n^3*r^2-225989190*n^2*r^3-1145549790*n*r^4+2095161390*r^5-1377810*n^4-2245320*n^3*r-26076330*n^2*r^2-187983180*n*r^3-269132220*r^4-1837080*n^3-3725190*n^2*r-20769210*n*r^2-55367550*r^3-1377810*n^2-2163672*n*r-5511240*r^2-551124*n-459270*r-91854)/r^6 The limit of the standardized moment is, 15 Theorem, 7 Central moment, 7, of X_n is -(1/73242187500)*(-1400000*F(n+1)^6*F(n)*n^10-1400000*F(n+1)^5*F(n)^2*n^10-28700000*F(n+1)^6*F(n)*n^9+175000*F(n+1)^5*F(n)^2*n^9+9450000*F(n+1)^4*F(n)^3*n^9-32201670*F(n+1)^6*F(n)*n^8+219854400*F(n+1)^5*F(n)^2*n^8+69003900*F(n+1)^4*F(n)^3*n^8-9043650*F(n+1)^3*F(n)^4*n^8-1224720*F(n+1)^2*F(n)^5*n^8-408240*F(n+1)*F(n)^6*n^8+2204518572*F(n+1)^6*F(n)*n^7+1156436592*F(n+1)^5*F(n)^2*n^7-75928860*F(n+1)^4*F(n)^3*n^7-75615120*F(n+1)^3*F(n)^4*n^7-10553004*F(n+1)^2*F(n)^5*n^7-2714796*F(n+1)*F(n)^6*n^7+8710524312*F(n+1)^6*F(n)*n^6-3214464666*F(n+1)^5*F(n)^2*n^6-1581725880*F(n+1)^4*F(n)^3*n^6-230101830*F(n+1)^3*F(n)^4*n^6-37251900*F(n+1)^2*F(n)^5*n^6-6797196*F(n+1)*F(n)^6*n^6-46566115680*F(n+1)^6*F(n)*n^5-28695881508*F(n+1)^5*F(n)^2*n^5-3240559980*F(n+1)^4*F(n)^3*n^5-265560120*F(n+1)^3*F(n)^4*n^5-57051540*F(n+1)^2*F(n)^5*n^5-6633900*F(n+1)*F(n)^6*n^5-238625059750*F(n+1)^6*F(n)*n^4-20970289900*F(n+1)^5*F(n)^2*n^4+1460622240*F(n+1)^4*F(n)^3*n^4+227561670*F(n+1)^3*F(n)^4*n^4+4025000*n^10*F(n+1)^7+30537500*n^9*F(n+1)^7-311150535*n^8*F(n+1)^7-2235860532*n^7*F(n+1)^7+157464*F(n)^7*n^7+6132861210*n^6*F(n+1)^7+1102248*F(n)^7*n^6+36006417300*n^5*F(n+1)^7+3306744*F(n)^7*n^5-6886200125*n^4*F(n+1)^7+5511240*F(n)^7*n^4+72206495200*n^3*F(n+1)^7+5511240*F(n)^7*n^3-117276064350*n^2*F(n+1)^7+3306744*F(n)^7*n^2-1165761967500*n*F(n+1)^7+1102248*F(n)^7*n-632034022500*F(n)*F(n+1)^6-20951613900*F(n+1)^5*F(n)^2+1345661100*F(n+1)^4*F(n)^3+184558500*F(n+1)^3*F(n)^4+13778100*F(n+1)^2*F(n)^5+918540*F(n+1)*F(n)^6+157464*F(n)^7-10103940*F(n+1)^2*F(n)^5*n^4+2347380*F(n+1)*F(n)^6*n^4+165139944200*F(n+1)^6*F(n)*n^3+109445543900*F(n+1)^5*F(n)^2*n^3+11677043700*F(n+1)^4*F(n)^3*n^3+1103896080*F(n+1)^3*F(n)^4*n^3+85832460*F(n+1)^2*F(n)^5*n^3+11941020*F(n+1)*F(n)^6*n^3+1311015214800*F(n+1)^6*F(n)*n^2+167552779650*F(n+1)^5*F(n)^2*n^2+14401270800*F(n+1)^4*F(n)^3*n^2+1407549150*F(n+1)^3*F(n)^4*n^2+119063196*F(n+1)^2*F(n)^5*n^2+11777724*F(n+1)*F(n)^6*n^2+328283408100*F(n+1)^6*F(n)*n+40728591600*F(n+1)^5*F(n)^2*n+7324827300*F(n+1)^4*F(n)^3*n+817803000*F(n+1)^3*F(n)^4*n+66032820*F(n+1)^2*F(n)^5*n+5245884*F(n+1)*F(n)^6*n)/F(n+1)^7 which is asymptotic to -(1/73242187500)*(4025000*n^10*r^7-1400000*n^10*r^6+30537500*n^9*r^7-1400000*n^10*r^5-28700000*n^9*r^6-311150535*n^8*r^7+175000*n^9*r^5-32201670*n^8*r^6-2235860532*n^7*r^7+9450000*n^9*r^4+219854400*n^8*r^5+2204518572*n^7*r^6+6132861210*n^6*r^7+69003900*n^8*r^4+1156436592*n^7*r^5+8710524312*n^6*r^6+36006417300*n^5*r^7-9043650*n^8*r^3-75928860*n^7*r^4-3214464666*n^6*r^5-46566115680*n^5*r^6-6886200125*n^4*r^7-1224720*n^8*r^2-75615120*n^7*r^3-1581725880*n^6*r^4-28695881508*n^5*r^5-238625059750*n^4*r^6+72206495200*n^3*r^7-408240*n^8*r-10553004*n^7*r^2-230101830*n^6*r^3-3240559980*n^5*r^4-20970289900*n^4*r^5+165139944200*n^3*r^6-117276064350*n^2*r^7-2714796*n^7*r-37251900*n^6*r^2-265560120*n^5*r^3+1460622240*n^4*r^4+109445543900*n^3*r^5+1311015214800*n^2*r^6-1165761967500*n*r^7+157464*n^7-6797196*n^6*r-57051540*n^5*r^2+227561670*n^4*r^3+11677043700*n^3*r^4+167552779650*n^2*r^5+328283408100*n*r^6+1102248*n^6-6633900*n^5*r-10103940*n^4*r^2+1103896080*n^3*r^3+14401270800*n^2*r^4+40728591600*n*r^5-632034022500*r^6+3306744*n^5+2347380*n^4*r+85832460*n^3*r^2+1407549150*n^2*r^3+7324827300*n*r^4-20951613900*r^5+5511240*n^4+11941020*n^3*r+119063196*n^2*r^2+817803000*n*r^3+1345661100*r^4+5511240*n^3+11777724*n^2*r+66032820*n*r^2+184558500*r^3+3306744*n^2+5245884*n*r+13778100*r^2+1102248*n+918540*r+157464)/r^7 The limit of the standardized moment is, 0 Theorem, 8 Central moment, 8, of X_n is (1/4119873046875)*(83475000*F(n+1)^7*F(n)*n^11+56700000*F(n+1)^6*F(n)^2*n^11+37800000*F(n+1)^5*F(n)^3*n^11+1250628750*F(n+1)^7*F(n)*n^10+777498750*F(n+1)^6*F(n)^2*n^10+58590000*F(n+1)^5*F(n)^3*n^10-178605000*F(n+1)^4*F(n)^4*n^10+6119834580*F(n+1)^7*F(n)*n^9-1976474520*F(n+1)^6*F(n)^2*n^9-5722385400*F(n+1)^5*F(n)^3*n^9-1490586300*F(n+1)^4*F(n)^4*n^9+131045040*F(n+1)^3*F(n)^5*n^9+12859560*F(n+1)^2*F(n)^6*n^9+3674160*F(n+1)*F(n)^7*n^9-1240029*F(n)^8-64223421129*F(n+1)^7*F(n)*n^8-114858583038*F(n+1)^6*F(n)^2*n^8-37169123832*F(n+1)^5*F(n)^3*n^8+23167620*F(n+1)^4*F(n)^4*n^8+1218259602*F(n+1)^3*F(n)^5*n^8+122900652*F(n+1)^2*F(n)^6*n^8+28107324*F(n+1)*F(n)^7*n^8-1245907419264*F(n+1)^7*F(n)*n^7-539510731596*F(n+1)^6*F(n)^2*n^7+57889653804*F(n+1)^5*F(n)^3*n^7+30805586280*F(n+1)^4*F(n)^4*n^7+4360717620*F(n+1)^3*F(n)^5*n^7+495827892*F(n+1)^2*F(n)^6*n^7+85607928*F(n+1)*F(n)^7*n^7-3535227268020*F(n+1)^7*F(n)*n^6+2197300331142*F(n+1)^6*F(n)^2*n^6+896435908704*F(n+1)^5*F(n)^3*n^6+89923994370*F(n+1)^4*F(n)^4*n^6+6988354380*F(n+1)^3*F(n)^5*n^6+965385540*F(n+1)^2*F(n)^6*n^6+120879864*F(n+1)*F(n)^7*n^6+32012642816910*F(n+1)^7*F(n)*n^5+16424939666520*F(n+1)^6*F(n)^2*n^5+1413664492968*F(n+1)^5*F(n)^3*n^5+32828160330*F(n+1)^4*F(n)^4*n^5+505401120*F(n+1)^3*F(n)^5*n^5+642059460*F(n+1)^2*F(n)^6*n^5+38578680*F(n+1)*F(n)^7*n^5+141746564748600*F(n+1)^7*F(n)*n^4+5172000809850*F(n+1)^6*F(n)^2*n^4-2444822484300*F(n+1)^5*F(n)^3*n^4-245318356080*F(n+1)^4*F(n)^4*n^4-18439690500*F(n+1)^3*F(n)^5*n^4-899250660*F(n+1)^2*F(n)^6*n^4-128595600*F(n+1)*F(n)^7*n^4-169497243123300*F(n+1)^7*F(n)*n^3-84156591319200*F(n+1)^6*F(n)^2*n^3-7774663124700*F(n+1)^5*F(n)^3*n^3-484196624100*F(n+1)^4*F(n)^4*n^3-34456047948*F(n+1)^3*F(n)^5*n^3-2261629188*F(n+1)^2*F(n)^6*n^3-213468696*F(n+1)*F(n)^7*n^3-947026247061150*F(n+1)^7*F(n)*n^2-97441387435800*F(n+1)^6*F(n)^2*n^2-5915093396400*F(n+1)^5*F(n)^3*n^2-400613311350*F(n+1)^4*F(n)^4*n^2-30319882740*F(n+1)^3*F(n)^5*n^2-2015460468*F(n+1)^2*F(n)^6*n^2-153212472*F(n+1)*F(n)^7*n^2-51588408577500*F(n+1)^7*F(n)*n+12216751994700*F(n+1)^6*F(n)^2*n-626103367200*F(n+1)^5*F(n)^3*n-158331546450*F(n+1)^4*F(n)^4*n-13585614840*F(n+1)^3*F(n)^5*n-864346140*F(n+1)^2*F(n)^6*n-55479816*F(n+1)*F(n)^7*n+8750000*n^12*F(n+1)^8+137287500*n^11*F(n+1)^8-1814386250*n^10*F(n+1)^8-23552302680*n^9*F(n+1)^8+200412615981*n^8*F(n+1)^8-1240029*F(n)^8*n^8+1838926219680*n^7*F(n+1)^8-9920232*F(n)^8*n^7-4729170873770*n^6*F(n+1)^8-34720812*F(n)^8*n^6-37394267725500*n^5*F(n+1)^8-69441624*F(n)^8*n^5+21999794253575*n^4*F(n+1)^8-86802030*F(n)^8*n^4+122856886859850*n^3*F(n+1)^8-69441624*F(n)^8*n^3+22038519763125*n^2*F(n+1)^8-34720812*F(n)^8*n^2+381073408813125*n*F(n+1)^8-9920232*F(n)^8*n+618565169379375*F(n)*F(n+1)^7+34129837215000*F(n+1)^6*F(n)^2+565693575300*F(n+1)^5*F(n)^3-24221899800*F(n+1)^4*F(n)^4-2491539750*F(n+1)^3*F(n)^5-148803480*F(n+1)^2*F(n)^6-8266860*F(n+1)*F(n)^7)/F(n+1)^8 which is asymptotic to (1/4119873046875)*(8750000*n^12*r^8+137287500*n^11*r^8+83475000*n^11*r^7-1814386250*n^10*r^8+56700000*n^11*r^6+1250628750*n^10*r^7-23552302680*n^9*r^8+37800000*n^11*r^5+777498750*n^10*r^6+6119834580*n^9*r^7+200412615981*n^8*r^8+58590000*n^10*r^5-1976474520*n^9*r^6-64223421129*n^8*r^7+1838926219680*n^7*r^8-178605000*n^10*r^4-5722385400*n^9*r^5-114858583038*n^8*r^6-1245907419264*n^7*r^7-4729170873770*n^6*r^8-1490586300*n^9*r^4-37169123832*n^8*r^5-539510731596*n^7*r^6-3535227268020*n^6*r^7-37394267725500*n^5*r^8+131045040*n^9*r^3+23167620*n^8*r^4+57889653804*n^7*r^5+2197300331142*n^6*r^6+32012642816910*n^5*r^7+21999794253575*n^4*r^8+12859560*n^9*r^2+1218259602*n^8*r^3+30805586280*n^7*r^4+896435908704*n^6*r^5+16424939666520*n^5*r^6+141746564748600*n^4*r^7+122856886859850*n^3*r^8+3674160*n^9*r+122900652*n^8*r^2+4360717620*n^7*r^3+89923994370*n^6*r^4+1413664492968*n^5*r^5+5172000809850*n^4*r^6-169497243123300*n^3*r^7+22038519763125*n^2*r^8+28107324*n^8*r+495827892*n^7*r^2+6988354380*n^6*r^3+32828160330*n^5*r^4-2444822484300*n^4*r^5-84156591319200*n^3*r^6-947026247061150*n^2*r^7+381073408813125*n*r^8-1240029*n^8+85607928*n^7*r+965385540*n^6*r^2+505401120*n^5*r^3-245318356080*n^4*r^4-7774663124700*n^3*r^5-97441387435800*n^2*r^6-51588408577500*n*r^7-9920232*n^7+120879864*n^6*r+642059460*n^5*r^2-18439690500*n^4*r^3-484196624100*n^3*r^4-5915093396400*n^2*r^5+12216751994700*n*r^6+618565169379375*r^7-34720812*n^6+38578680*n^5*r-899250660*n^4*r^2-34456047948*n^3*r^3-400613311350*n^2*r^4-626103367200*n*r^5+34129837215000*r^6-69441624*n^5-128595600*n^4*r-2261629188*n^3*r^2-30319882740*n^2*r^3-158331546450*n*r^4+565693575300*r^5-86802030*n^4-213468696*n^3*r-2015460468*n^2*r^2-13585614840*n*r^3-24221899800*r^4-69441624*n^3-153212472*n^2*r-864346140*n*r^2-2491539750*r^3-34720812*n^2-55479816*n*r-148803480*r^2-9920232*n-8266860*r-1240029)/r^8 The limit of the standardized moment is, 105 Theorem, 9 Central moment, 9, of X_n is -(1/7629394531250)*(35000000*F(n+1)^8*F(n)*n^13+95900000*F(n+1)^8*F(n)*n^12-384300000*F(n+1)^7*F(n)^2*n^12-50400000*F(n+1)^6*F(n)^3*n^12-25200000*F(n+1)^5*F(n)^4*n^12-9678492500*F(n+1)^8*F(n)*n^11-4751932500*F(n+1)^7*F(n)^2*n^11-545265000*F(n+1)^6*F(n)^3*n^11-72765000*F(n+1)^5*F(n)^4*n^11+91854000*F(n+1)^4*F(n)^5*n^11-80307901310*F(n+1)^8*F(n)*n^10-1454197770*F(n+1)^7*F(n)^2*n^10+3236664420*F(n+1)^6*F(n)^3*n^10+3694555800*F(n+1)^5*F(n)^4*n^10+860671980*F(n+1)^4*F(n)^5*n^10-54806220*F(n+1)^3*F(n)^6*n^10-4199040*F(n+1)^2*F(n)^7*n^10-1049760*F(n+1)*F(n)^8*n^10+207952013862*F(n+1)^8*F(n)*n^9+268898874606*F(n+1)^7*F(n)^2*n^9+117774602568*F(n+1)^6*F(n)^3*n^9+28524625704*F(n+1)^5*F(n)^4*n^9+787678668*F(n+1)^4*F(n)^5*n^9-562207716*F(n+1)^3*F(n)^6*n^9-44142408*F(n+1)^2*F(n)^7*n^9-9080424*F(n+1)*F(n)^8*n^9+4648045010682*F(n+1)^8*F(n)*n^8+2547362241792*F(n+1)^7*F(n)^2*n^8+636919943364*F(n+1)^6*F(n)^3*n^8-14584896234*F(n+1)^5*F(n)^4*n^8-15674272740*F(n+1)^4*F(n)^5*n^8-2313965556*F(n+1)^3*F(n)^6*n^8-200346696*F(n+1)^2*F(n)^7*n^8-32490072*F(n+1)*F(n)^8*n^8+23126869745140*F(n+1)^8*F(n)*n^7+7076310298416*F(n+1)^7*F(n)^2*n^7-1725456260016*F(n+1)^6*F(n)^3*n^7-648610194276*F(n+1)^5*F(n)^4*n^7-61591985280*F(n+1)^4*F(n)^5*n^7-4681083960*F(n+1)^3*F(n)^6*n^7-469557648*F(n+1)^2*F(n)^7*n^7-58996512*F(n+1)*F(n)^8*n^7+567731447080*F(n+1)^8*F(n)*n^6-60802843864770*F(n+1)^7*F(n)^2*n^6-19014811527852*F(n+1)^6*F(n)^3*n^6-1575911743434*F(n+1)^5*F(n)^4*n^6-62549716320*F(n+1)^4*F(n)^5*n^6-3074659560*F(n+1)^3*F(n)^6*n^6-503359920*F(n+1)^2*F(n)^7*n^6-45559584*F(n+1)*F(n)^8*n^6-828578718160300*F(n+1)^8*F(n)*n^5-352618202792520*F(n+1)^7*F(n)^2*n^5-22339747397520*F(n+1)^6*F(n)^3*n^5+681876248004*F(n+1)^5*F(n)^4*n^5+108660424320*F(n+1)^4*F(n)^5*n^5+7299739440*F(n+1)^3*F(n)^6*n^5+124921440*F(n+1)^2*F(n)^7*n^5+25719120*F(n+1)*F(n)^8*n^5-2822945940076600*F(n+1)^8*F(n)*n^4+54407817549450*F(n+1)^7*F(n)^2*n^4+80064726563700*F(n+1)^6*F(n)^3*n^4+6930223411050*F(n+1)^5*F(n)^4*n^4+371845689768*F(n+1)^4*F(n)^5*n^4+21429374904*F(n+1)^3*F(n)^6*n^4+1084612032*F(n+1)^2*F(n)^7*n^4+97732656*F(n+1)*F(n)^8*n^4+5897162104824900*F(n+1)^8*F(n)*n^3+2304764790822900*F(n+1)^7*F(n)^2*n^3+186052470265800*F(n+1)^6*F(n)^3*n^3+9322239267900*F(n+1)^5*F(n)^4*n^3+449704120320*F(n+1)^4*F(n)^5*n^3+26131483224*F(n+1)^3*F(n)^6*n^3+1441215504*F(n+1)^2*F(n)^7*n^3+104766048*F(n+1)*F(n)^8*n^3+24769912252173750*F(n+1)^8*F(n)*n^2+2129464511242200*F(n+1)^7*F(n)^2*n^2+89592983101800*F(n+1)^6*F(n)^3*n^2+4488671623050*F(n+1)^5*F(n)^4*n^2+283014319140*F(n+1)^4*F(n)^5*n^2+17650562580*F(n+1)^3*F(n)^6*n^2+964414512*F(n+1)^2*F(n)^7*n^2+59626368*F(n+1)*F(n)^8*n^2-3391917268421250*F(n+1)^8*F(n)*n-1071002375358750*F(n+1)^7*F(n)^2*n-44951328815400*F(n+1)^6*F(n)^3*n+70981517700*F(n+1)^5*F(n)^4*n+91955549700*F(n+1)^4*F(n)^5*n+6445191060*F(n+1)^3*F(n)^6*n+338285160*F(n+1)^2*F(n)^7*n+17500000*n^13*F(n+1)^9+466331250*n^12*F(n+1)^9+212372000*n^11*F(n+1)^9+22457852190*n^10*F(n+1)^9+526298229624*n^9*F(n+1)^9+314928*F(n)^9*n^9-4644635434515*n^8*F(n+1)^9+2834352*F(n)^9*n^8-52424857809880*n^7*F(n+1)^9+11337408*F(n)^9*n^7+133395475712100*n^6*F(n+1)^9+26453952*F(n)^9*n^6+1290034480554700*n^5*F(n+1)^9+39680928*F(n)^9*n^5-918336819427200*n^4*F(n+1)^9+39680928*F(n)^9*n^4-7623253171173750*n^3*F(n+1)^9+26453952*F(n)^9*n^3+618363346899375*n^2*F(n+1)^9+11337408*F(n)^9*n^2+1124896998431250*n*F(n+1)^9+2834352*F(n)^9*n-20252110580043750*F(n)*F(n+1)^8-1237130338758750*F(n+1)^7*F(n)^2-34129837215000*F(n+1)^6*F(n)^3-377129050200*F(n+1)^5*F(n)^4+12110949900*F(n+1)^4*F(n)^5+996615900*F(n+1)^3*F(n)^6+49601160*F(n+1)^2*F(n)^7+2361960*F(n+1)*F(n)^8+314928*F(n)^9+18213336*F(n+1)*F(n)^8*n)/F(n+1)^9 which is asymptotic to -(1/7629394531250)*(17500000*n^13*r^9+35000000*n^13*r^8+466331250*n^12*r^9+95900000*n^12*r^8+212372000*n^11*r^9-384300000*n^12*r^7-9678492500*n^11*r^8+22457852190*n^10*r^9-50400000*n^12*r^6-4751932500*n^11*r^7-80307901310*n^10*r^8+526298229624*n^9*r^9-25200000*n^12*r^5-545265000*n^11*r^6-1454197770*n^10*r^7+207952013862*n^9*r^8-4644635434515*n^8*r^9-72765000*n^11*r^5+3236664420*n^10*r^6+268898874606*n^9*r^7+4648045010682*n^8*r^8-52424857809880*n^7*r^9+91854000*n^11*r^4+3694555800*n^10*r^5+117774602568*n^9*r^6+2547362241792*n^8*r^7+23126869745140*n^7*r^8+133395475712100*n^6*r^9+860671980*n^10*r^4+28524625704*n^9*r^5+636919943364*n^8*r^6+7076310298416*n^7*r^7+567731447080*n^6*r^8+1290034480554700*n^5*r^9-54806220*n^10*r^3+787678668*n^9*r^4-14584896234*n^8*r^5-1725456260016*n^7*r^6-60802843864770*n^6*r^7-828578718160300*n^5*r^8-918336819427200*n^4*r^9-4199040*n^10*r^2-562207716*n^9*r^3-15674272740*n^8*r^4-648610194276*n^7*r^5-19014811527852*n^6*r^6-352618202792520*n^5*r^7-2822945940076600*n^4*r^8-7623253171173750*n^3*r^9-1049760*n^10*r-44142408*n^9*r^2-2313965556*n^8*r^3-61591985280*n^7*r^4-1575911743434*n^6*r^5-22339747397520*n^5*r^6+54407817549450*n^4*r^7+5897162104824900*n^3*r^8+618363346899375*n^2*r^9-9080424*n^9*r-200346696*n^8*r^2-4681083960*n^7*r^3-62549716320*n^6*r^4+681876248004*n^5*r^5+80064726563700*n^4*r^6+2304764790822900*n^3*r^7+24769912252173750*n^2*r^8+1124896998431250*n*r^9+314928*n^9-32490072*n^8*r-469557648*n^7*r^2-3074659560*n^6*r^3+108660424320*n^5*r^4+6930223411050*n^4*r^5+186052470265800*n^3*r^6+2129464511242200*n^2*r^7-3391917268421250*n*r^8+2834352*n^8-58996512*n^7*r-503359920*n^6*r^2+7299739440*n^5*r^3+371845689768*n^4*r^4+9322239267900*n^3*r^5+89592983101800*n^2*r^6-1071002375358750*n*r^7-20252110580043750*r^8+11337408*n^7-45559584*n^6*r+124921440*n^5*r^2+21429374904*n^4*r^3+449704120320*n^3*r^4+4488671623050*n^2*r^5-44951328815400*n*r^6-1237130338758750*r^7+26453952*n^6+25719120*n^5*r+1084612032*n^4*r^2+26131483224*n^3*r^3+283014319140*n^2*r^4+70981517700*n*r^5-34129837215000*r^6+39680928*n^5+97732656*n^4*r+1441215504*n^3*r^2+17650562580*n^2*r^3+91955549700*n*r^4-377129050200*r^5+39680928*n^4+104766048*n^3*r+964414512*n^2*r^2+6445191060*n*r^3+12110949900*r^4+26453952*n^3+59626368*n^2*r+338285160*n*r^2+996615900*r^3+11337408*n^2+18213336*n*r+49601160*r^2+2834352*n+2361960*r+314928)/r^9 The limit of the standardized moment is, 0 Theorem, 10 Central moment, 10, of X_n is (1/18882751464843750)*(1925000000*n^15*F(n+1)^10+285140625000*n^14*F(n+1)^10+2133273312500*n^13*F(n+1)^10-45442874248750*n^12*F(n+1)^10-303810971198800*n^11*F(n+1)^10+723361329578668*n^10*F(n+1)^10-105225318*F(n)^10*n^10-8177207477636450*n^9*F(n+1)^10-1052253180*F(n)^10*n^9+144710064408374025*n^8*F(n+1)^10-4735139310*F(n)^10*n^8+2062213724442982000*n^7*F(n+1)^10-12627038160*F(n)^10*n^7-5481166440467524400*n^6*F(n+1)^10-22097316780*F(n)^10*n^6-63150492125874362000*n^5*F(n+1)^10-26516780136*F(n)^10*n^5+48433410095184021875*n^4*F(n+1)^10-22097316780*F(n)^10*n^4+495948807832345518750*n^3*F(n+1)^10-12627038160*F(n)^10*n^3-69267625043912625000*n^2*F(n+1)^10-4735139310*F(n)^10*n^2-566884956360404381250*n*F(n+1)^10-1052253180*F(n)^10*n+945847448685350268750*F(n)*F(n+1)^9+60148768422729937500*F(n+1)^8*F(n)^2+1837138553056743750*F(n+1)^7*F(n)^3+33788538842850000*F(n+1)^6*F(n)^4+280018319773500*F(n+1)^5*F(n)^5-7193904240600*F(n+1)^4*F(n)^6-493324870500*F(n+1)^3*F(n)^7-21045063600*F(n+1)^2*F(n)^8-876877650*F(n+1)*F(n)^9+1673197550638020*F(n+1)^5*F(n)^5*n^7+74690900984700*F(n+1)^4*F(n)^6*n^7+3916388183400*F(n+1)^3*F(n)^7*n^7+396894310560*F(n+1)^2*F(n)^8*n^7+38816450640*F(n+1)*F(n)^9*n^7+5240407512838843950*F(n+1)^9*F(n)*n^6+2630020829389712550*F(n+1)^8*F(n)^2*n^6+618359415498178200*F(n+1)^7*F(n)^3*n^6+41503025669531580*F(n+1)^6*F(n)^4*n^6+682268272699860*F(n+1)^5*F(n)^5*n^6-27881468792100*F(n+1)^4*F(n)^6*n^6-2108692278000*F(n+1)^3*F(n)^7*n^6+137767221900*F(n+1)^2*F(n)^8*n^6+7365772260*F(n+1)*F(n)^9*n^6+31553381419753965200*F(n+1)^9*F(n)*n^5+10460525478268338000*F(n+1)^8*F(n)^2*n^5+445908118882376700*F(n+1)^7*F(n)^3*n^5-57314707295452200*F(n+1)^6*F(n)^4*n^5-5701733245657548*F(n+1)^5*F(n)^5*n^5-289184028112980*F(n+1)^4*F(n)^6*n^5-14361315950520*F(n+1)^3*F(n)^7*n^5-535518923940*F(n+1)^2*F(n)^8*n^5-45831471840*F(n+1)*F(n)^9*n^5+56729643572548856250*F(n+1)^9*F(n)*n^4-9990985709879559000*F(n+1)^8*F(n)^2*n^4-3538330337703694500*F(n+1)^7*F(n)^3*n^4-266195665505954250*F(n+1)^6*F(n)^4*n^4-12206880749952900*F(n+1)^5*F(n)^5*n^4-493697978692380*F(n+1)^4*F(n)^6*n^4-23716649262240*F(n+1)^3*F(n)^7*n^4-1086470894520*F(n+1)^2*F(n)^8*n^4-75177643860*F(n+1)*F(n)^9*n^4-297743756323677056250*F(n+1)^9*F(n)*n^3-92708792625827688750*F(n+1)^8*F(n)^2*n^3-6685787253724029000*F(n+1)^7*F(n)^3*n^3-277256304223816500*F(n+1)^6*F(n)^4*n^3-10398769012892700*F(n+1)^5*F(n)^5*n^3-439527806001900*F(n+1)^4*F(n)^6*n^3-21781534012920*F(n+1)^3*F(n)^7*n^3-1027038076020*F(n+1)^2*F(n)^8*n^3-61030684440*F(n+1)*F(n)^9*n^3-912239928351138543750*F(n+1)^9*F(n)*n^2-65821675553791368750*F(n+1)^8*F(n)^2*n^2-1668433513160823750*F(n+1)^7*F(n)^3*n^2-47048223730761000*F(n+1)^6*F(n)^4*n^2-3456190784227500*F(n+1)^5*F(n)^5*n^2-224403505949700*F(n+1)^4*F(n)^6*n^2-11963707281900*F(n+1)^3*F(n)^7*n^2-554323077990*F(n+1)^2*F(n)^8*n^2-28897990110*F(n+1)*F(n)^9*n^2+361854418108035112500*F(n+1)^9*F(n)*n+69090974685766068750*F(n+1)^8*F(n)^2*n+3396416263073212500*F(n+1)^7*F(n)^3*n+77599700474917500*F(n+1)^6*F(n)^4*n+213633984940200*F(n+1)^5*F(n)^5*n-62084316086100*F(n+1)^4*F(n)^6*n-3688760849400*F(n+1)^3*F(n)^7*n-164755567350*F(n+1)^2*F(n)^8*n-7638578640*F(n+1)*F(n)^9*n+3850000000*F(n+1)^9*F(n)*n^15-72187500000*F(n+1)^9*F(n)*n^14-129937500000*F(n+1)^8*F(n)^2*n^14-4407590000000*F(n+1)^9*F(n)*n^13-848491875000*F(n+1)^8*F(n)^2*n^13+678273750000*F(n+1)^7*F(n)^3*n^13+46777500000*F(n+1)^6*F(n)^4*n^13+18711000000*F(n+1)^5*F(n)^5*n^13-16766399141250*F(n+1)^9*F(n)*n^12+33007551637500*F(n+1)^8*F(n)^2*n^12+8766337387500*F(n+1)^7*F(n)^3*n^12+443567643750*F(n+1)^6*F(n)^4*n^12+76527990000*F(n+1)^5*F(n)^5*n^12-55571670000*F(n+1)^4*F(n)^6*n^12+702439093624600*F(n+1)^9*F(n)*n^11+347579639025300*F(n+1)^8*F(n)^2*n^11+3670616525400*F(n+1)^7*F(n)^3*n^11-3816163513800*F(n+1)^6*F(n)^4*n^11-2649168066600*F(n+1)^5*F(n)^5*n^11-577137052800*F(n+1)^4*F(n)^6*n^11+27973479600*F(n+1)^3*F(n)^7*n^11+1753755300*F(n+1)^2*F(n)^8*n^11+389723400*F(n+1)*F(n)^9*n^11+5363726719090410*F(n+1)^9*F(n)*n^10-829039078661310*F(n+1)^8*F(n)^2*n^10-479314668148470*F(n+1)^7*F(n)^3*n^10-121274884979820*F(n+1)^6*F(n)^4*n^10-23855462151048*F(n+1)^5*F(n)^5*n^10-1010818365480*F(n+1)^4*F(n)^6*n^10+314216656380*F(n+1)^3*F(n)^7*n^10+20129213610*F(n+1)^2*F(n)^8*n^10+3760830810*F(n+1)*F(n)^9*n^10-28430811743541790*F(n+1)^9*F(n)*n^9-21004422635312820*F(n+1)^8*F(n)^2*n^9-4221644927795460*F(n+1)^7*F(n)^3*n^9-738975236473980*F(n+1)^6*F(n)^4*n^9-9975617770140*F(n+1)^5*F(n)^5*n^9+8924183757720*F(n+1)^4*F(n)^6*n^9+1460781455760*F(n+1)^3*F(n)^7*n^9+101503459530*F(n+1)^2*F(n)^8*n^9+15433046640*F(n+1)*F(n)^9*n^9-350152236789758700*F(n+1)^9*F(n)*n^8-79964306544057210*F(n+1)^8*F(n)^2*n^8-13024518757211610*F(n+1)^7*F(n)^3*n^8+1119783389196780*F(n+1)^6*F(n)^4*n^8+498287078059320*F(n+1)^5*F(n)^5*n^8+46485045198900*F(n+1)^4*F(n)^6*n^8+3541689342180*F(n+1)^3*F(n)^7*n^8+276781558680*F(n+1)^2*F(n)^8*n^8+33964394310*F(n+1)*F(n)^9*n^8-403544356779988600*F(n+1)^9*F(n)*n^7+63317673721585800*F(n+1)^8*F(n)^2*n^7+82919218408390980*F(n+1)^7*F(n)^3*n^7+20760683014366020*F(n+1)^6*F(n)^4*n^7-105225318*F(n)^10)/F(n+1)^10 which is asymptotic to (1/18882751464843750)*(1925000000*n^15*r^10+3850000000*n^15*r^9+285140625000*n^14*r^10-72187500000*n^14*r^9+2133273312500*n^13*r^10-129937500000*n^14*r^8-4407590000000*n^13*r^9-45442874248750*n^12*r^10-848491875000*n^13*r^8-16766399141250*n^12*r^9-303810971198800*n^11*r^10+678273750000*n^13*r^7+33007551637500*n^12*r^8+702439093624600*n^11*r^9+723361329578668*n^10*r^10+46777500000*n^13*r^6+8766337387500*n^12*r^7+347579639025300*n^11*r^8+5363726719090410*n^10*r^9-8177207477636450*n^9*r^10+18711000000*n^13*r^5+443567643750*n^12*r^6+3670616525400*n^11*r^7-829039078661310*n^10*r^8-28430811743541790*n^9*r^9+144710064408374025*n^8*r^10+76527990000*n^12*r^5-3816163513800*n^11*r^6-479314668148470*n^10*r^7-21004422635312820*n^9*r^8-350152236789758700*n^8*r^9+2062213724442982000*n^7*r^10-55571670000*n^12*r^4-2649168066600*n^11*r^5-121274884979820*n^10*r^6-4221644927795460*n^9*r^7-79964306544057210*n^8*r^8-403544356779988600*n^7*r^9-5481166440467524400*n^6*r^10-577137052800*n^11*r^4-23855462151048*n^10*r^5-738975236473980*n^9*r^6-13024518757211610*n^8*r^7+63317673721585800*n^7*r^8+5240407512838843950*n^6*r^9-63150492125874362000*n^5*r^10+27973479600*n^11*r^3-1010818365480*n^10*r^4-9975617770140*n^9*r^5+1119783389196780*n^8*r^6+82919218408390980*n^7*r^7+2630020829389712550*n^6*r^8+31553381419753965200*n^5*r^9+48433410095184021875*n^4*r^10+1753755300*n^11*r^2+314216656380*n^10*r^3+8924183757720*n^9*r^4+498287078059320*n^8*r^5+20760683014366020*n^7*r^6+618359415498178200*n^6*r^7+10460525478268338000*n^5*r^8+56729643572548856250*n^4*r^9+495948807832345518750*n^3*r^10+389723400*n^11*r+20129213610*n^10*r^2+1460781455760*n^9*r^3+46485045198900*n^8*r^4+1673197550638020*n^7*r^5+41503025669531580*n^6*r^6+445908118882376700*n^5*r^7-9990985709879559000*n^4*r^8-297743756323677056250*n^3*r^9-69267625043912625000*n^2*r^10+3760830810*n^10*r+101503459530*n^9*r^2+3541689342180*n^8*r^3+74690900984700*n^7*r^4+682268272699860*n^6*r^5-57314707295452200*n^5*r^6-3538330337703694500*n^4*r^7-92708792625827688750*n^3*r^8-912239928351138543750*n^2*r^9-566884956360404381250*n*r^10-105225318*n^10+15433046640*n^9*r+276781558680*n^8*r^2+3916388183400*n^7*r^3-27881468792100*n^6*r^4-5701733245657548*n^5*r^5-266195665505954250*n^4*r^6-6685787253724029000*n^3*r^7-65821675553791368750*n^2*r^8+361854418108035112500*n*r^9-1052253180*n^9+33964394310*n^8*r+396894310560*n^7*r^2-2108692278000*n^6*r^3-289184028112980*n^5*r^4-12206880749952900*n^4*r^5-277256304223816500*n^3*r^6-1668433513160823750*n^2*r^7+69090974685766068750*n*r^8+945847448685350268750*r^9-4735139310*n^8+38816450640*n^7*r+137767221900*n^6*r^2-14361315950520*n^5*r^3-493697978692380*n^4*r^4-10398769012892700*n^3*r^5-47048223730761000*n^2*r^6+3396416263073212500*n*r^7+60148768422729937500*r^8-12627038160*n^7+7365772260*n^6*r-535518923940*n^5*r^2-23716649262240*n^4*r^3-439527806001900*n^3*r^4-3456190784227500*n^2*r^5+77599700474917500*n*r^6+1837138553056743750*r^7-22097316780*n^6-45831471840*n^5*r-1086470894520*n^4*r^2-21781534012920*n^3*r^3-224403505949700*n^2*r^4+213633984940200*n*r^5+33788538842850000*r^6-26516780136*n^5-75177643860*n^4*r-1027038076020*n^3*r^2-11963707281900*n^2*r^3-62084316086100*n*r^4+280018319773500*r^5-22097316780*n^4-61030684440*n^3*r-554323077990*n^2*r^2-3688760849400*n*r^3-7193904240600*r^4-12627038160*n^3-28897990110*n^2*r-164755567350*n*r^2-493324870500*r^3-4735139310*n^2-7638578640*n*r-21045063600*r^2-1052253180*n-876877650*r-105225318)/r^10 The limit of the standardized moment is, 945 Theorem, 11 Central moment, 11, of X_n is -(1/5722045898437500)*(-5967432459068408*F(n+1)^10*F(n)*n^11-2765893550852380*F(n+1)^9*F(n)^2*n^11+120932955592020*F(n+1)^8*F(n)^3*n^11+69266194214580*F(n+1)^7*F(n)^4*n^11+12666629374344*F(n+1)^6*F(n)^5*n^11+2114648192448*F(n+1)^5*F(n)^6*n^11+107912966040*F(n+1)^4*F(n)^7*n^11-19966828860*F(n+1)^3*F(n)^8*n^11-1078234740*F(n+1)^2*F(n)^9*n^11-184469076*F(n+1)*F(n)^10*n^11-40938901723796208*F(n+1)^10*F(n)*n^10+11347165196888290*F(n+1)^9*F(n)^2*n^10+4835495511914760*F(n+1)^8*F(n)^3*n^10+634905045658620*F(n+1)^7*F(n)^4*n^10+85623094145160*F(n+1)^6*F(n)^5*n^10+2682917781588*F(n+1)^5*F(n)^6*n^10-529931445120*F(n+1)^4*F(n)^7*n^10-103394339730*F(n+1)^3*F(n)^8*n^10-5980089060*F(n+1)^2*F(n)^9*n^10-853061220*F(n+1)*F(n)^10*n^10+314198164455357820*F(n+1)^10*F(n)*n^9+187778790700196080*F(n+1)^9*F(n)^2*n^9+20464073915319540*F(n+1)^8*F(n)^3*n^9+2217679304997420*F(n+1)^7*F(n)^4*n^9-41099103254880*F(n+1)^6*F(n)^5*n^9-39397682408040*F(n+1)^5*F(n)^6*n^9-3725874064440*F(n+1)^4*F(n)^7*n^9-290836139220*F(n+1)^3*F(n)^8*n^9-18537843060*F(n+1)^2*F(n)^9*n^9-2195441820*F(n+1)*F(n)^10*n^9+3108982924590369970*F(n+1)^10*F(n)*n^8+287281369381150870*F(n+1)^9*F(n)^2*n^8-5751862071719940*F(n+1)^8*F(n)^3*n^8-9612756688647420*F(n+1)^7*F(n)^4*n^8-2204243660761560*F(n+1)^6*F(n)^5*n^8-175177689508800*F(n+1)^5*F(n)^6*n^8-8151711563160*F(n+1)^4*F(n)^7*n^8-432880214580*F(n+1)^3*F(n)^8*n^8-32775737940*F(n+1)^2*F(n)^9*n^8-3234704220*F(n+1)*F(n)^10*n^8-2247742040192063580*F(n+1)^10*F(n)*n^7-2828359203479940020*F(n+1)^9*F(n)^2*n^7-558968956496521560*F(n+1)^8*F(n)^3*n^7-94008116339173080*F(n+1)^7*F(n)^4*n^7-6273760682657160*F(n+1)^6*F(n)^5*n^7-190567235426040*F(n+1)^5*F(n)^6*n^7-3142487003040*F(n+1)^4*F(n)^7*n^7-105869083320*F(n+1)^3*F(n)^8*n^7-25228094760*F(n+1)^2*F(n)^9*n^7-2052543240*F(n+1)*F(n)^10*n^7-71073893153795780820*F(n+1)^10*F(n)*n^6-15783821377769337860*F(n+1)^9*F(n)^2*n^6+6352500000*n^16*F(n+1)^11+85614375000*n^15*F(n+1)^11-2884958670000*n^14*F(n+1)^11-33708906121000*n^13*F(n+1)^11+457306629273090*n^12*F(n+1)^11+4485227039945116*n^11*F(n+1)^11+4251528*F(n)^11*n^11-18147688804265790*n^10*F(n+1)^11+46766808*F(n)^11*n^10-108748725782549160*n^9*F(n+1)^11+233834040*F(n)^11*n^9-407422322557337175*n^8*F(n+1)^11+701502120*F(n)^11*n^8-8966152305654639920*n^7*F(n+1)^11+1403004240*F(n)^11*n^7+28987149579961942380*n^6*F(n+1)^11+1964205936*F(n)^11*n^6+397337112180436670000*n^5*F(n+1)^11+1964205936*F(n)^11*n^5-325026354207410191875*n^4*F(n+1)^11+1403004240*F(n)^11*n^4-3924002923366713825000*n^3*F(n+1)^11+701502120*F(n)^11*n^3+640628369201426276250*n^2*F(n+1)^11+233834040*F(n)^11*n^2+6823323752165242132500*n*F(n+1)^11+46766808*F(n)^11*n-5687785861922231572500*F(n)*F(n+1)^10-378338979474140107500*F(n+1)^9*F(n)^2-12029753684545987500*F(n+1)^8*F(n)^3-244951807074232500*F(n+1)^7*F(n)^4-3378853884285000*F(n+1)^6*F(n)^5-22401465581880*F(n+1)^5*F(n)^6+479593616040*F(n+1)^4*F(n)^7+28189992600*F(n+1)^3*F(n)^8+1052253180*F(n+1)^2*F(n)^9+38972340*F(n+1)*F(n)^10+4251528*F(n)^11-2603864291008689720*F(n+1)^8*F(n)^3*n^6-142401995117975340*F(n+1)^7*F(n)^4*n^6+1557466097843304*F(n+1)^6*F(n)^5*n^6+403226655514848*F(n+1)^5*F(n)^6*n^6+21340323821520*F(n+1)^4*F(n)^7*n^6+947901131100*F(n+1)^3*F(n)^8*n^6+21642639480*F(n+1)^2*F(n)^9*n^6+1709586648*F(n+1)*F(n)^10*n^6-148446976399651497040*F(n+1)^10*F(n)*n^5-30460293953213899280*F(n+1)^9*F(n)^2*n^5-10903523192931600*F(n+1)^8*F(n)^3*n^5+414449183674464840*F(n+1)^7*F(n)^4*n^5+32525434394081640*F(n+1)^6*F(n)^5*n^5+1442778530829768*F(n+1)^5*F(n)^6*n^5+52642647493920*F(n+1)^4*F(n)^7*n^5+2189359248120*F(n+1)^3*F(n)^8*n^5+82543416120*F(n+1)^2*F(n)^9*n^5+5378182920*F(n+1)*F(n)^10*n^5+193931338668712521250*F(n+1)^10*F(n)*n^4+105640254110487223050*F(n+1)^9*F(n)^2*n^4+20705832032882703300*F(n+1)^8*F(n)^3*n^4+1372276729152237150*F(n+1)^7*F(n)^4*n^4+54771613735055580*F(n+1)^6*F(n)^5*n^4+1823577041678040*F(n+1)^5*F(n)^6*n^4+62690787763560*F(n+1)^4*F(n)^7*n^4+2612043865530*F(n+1)^3*F(n)^8*n^4+106498414440*F(n+1)^2*F(n)^9*n^4+6053703480*F(n+1)*F(n)^10*n^4+1997514615475135515000*F(n+1)^10*F(n)*n^3+487118881780418827500*F(n+1)^9*F(n)^2*n^3+31969867785096354300*F(n+1)^8*F(n)^3*n^3+1127067701020064100*F(n+1)^7*F(n)^4*n^3+32863670278084800*F(n+1)^6*F(n)^5*n^3+1119853637294040*F(n+1)^5*F(n)^6*n^3+44546109216840*F(n+1)^4*F(n)^7*n^3+1934545098420*F(n+1)^3*F(n)^8*n^3+79377996060*F(n+1)^2*F(n)^9*n^3+3996829980*F(n+1)*F(n)^10*n^3+3809265668637014055000*F(n+1)^10*F(n)*n^2+218450518635046818750*F(n+1)^9*F(n)^2*n^2-423138594646845000*F(n+1)^8*F(n)^3*n^2-221879162737306800*F(n+1)^7*F(n)^4*n^2-2842529281471440*F(n+1)^6*F(n)^5*n^2+263902084484940*F(n+1)^5*F(n)^6*n^2+19191579525360*F(n+1)^4*F(n)^7*n^2+896199991830*F(n+1)^3*F(n)^8*n^2+36023432940*F(n+1)^2*F(n)^9*n^2+1623847500*F(n+1)*F(n)^10*n^2-3599722772450754067500*F(n+1)^10*F(n)*n-523748935534422315000*F(n+1)^9*F(n)^2*n-25772496086754202500*F(n+1)^8*F(n)^3*n-695729920991242500*F(n+1)^7*F(n)^4*n-11097384698066040*F(n+1)^6*F(n)^5*n-38762554620240*F(n+1)^5*F(n)^6*n+4631348751480*F(n+1)^4*F(n)^7*n+239193458460*F(n+1)^3*F(n)^8*n+9297068220*F(n+1)^2*F(n)^9*n+378464724*F(n+1)*F(n)^10*n-42831250000*F(n+1)^10*F(n)*n^15-1540000000*F(n+1)^10*F(n)*n^16-1540000000*F(n+1)^9*F(n)^2*n^16+16940000000*F(n+1)^9*F(n)^2*n^15+27720000000*F(n+1)^8*F(n)^3*n^15+690669897500*F(n+1)^10*F(n)*n^14+1494120237500*F(n+1)^9*F(n)^2*n^14+228066300000*F(n+1)^8*F(n)^3*n^14-97609050000*F(n+1)^7*F(n)^4*n^14-4490640000*F(n+1)^6*F(n)^5*n^14-1496880000*F(n+1)^5*F(n)^6*n^14+34029347698500*F(n+1)^10*F(n)*n^13+7779050163500*F(n+1)^9*F(n)^2*n^13-6704314155000*F(n+1)^8*F(n)^3*n^13-1342389510000*F(n+1)^7*F(n)^4*n^13-40078962000*F(n+1)^6*F(n)^5*n^13-7821198000*F(n+1)^5*F(n)^6*n^13+3752892000*F(n+1)^4*F(n)^7*n^13+92361354930600*F(n+1)^10*F(n)*n^12-288138340692700*F(n+1)^9*F(n)^2*n^12-81775258220700*F(n+1)^8*F(n)^3*n^12-1364496868350*F(n+1)^7*F(n)^4*n^12+415128714660*F(n+1)^6*F(n)^5*n^12+203475175200*F(n+1)^5*F(n)^6*n^12+42768534600*F(n+1)^4*F(n)^7*n^12-1634673150*F(n+1)^3*F(n)^8*n^12-86605200*F(n+1)^2*F(n)^9*n^12-17321040*F(n+1)*F(n)^10*n^12)/F(n+1)^11 which is asymptotic to -(1/5722045898437500)*(6352500000*n^16*r^11-1540000000*n^16*r^10+85614375000*n^15*r^11-1540000000*n^16*r^9-42831250000*n^15*r^10-2884958670000*n^14*r^11+16940000000*n^15*r^9+690669897500*n^14*r^10-33708906121000*n^13*r^11+27720000000*n^15*r^8+1494120237500*n^14*r^9+34029347698500*n^13*r^10+457306629273090*n^12*r^11+228066300000*n^14*r^8+7779050163500*n^13*r^9+92361354930600*n^12*r^10+4485227039945116*n^11*r^11-97609050000*n^14*r^7-6704314155000*n^13*r^8-288138340692700*n^12*r^9-5967432459068408*n^11*r^10-18147688804265790*n^10*r^11-4490640000*n^14*r^6-1342389510000*n^13*r^7-81775258220700*n^12*r^8-2765893550852380*n^11*r^9-40938901723796208*n^10*r^10-108748725782549160*n^9*r^11-1496880000*n^14*r^5-40078962000*n^13*r^6-1364496868350*n^12*r^7+120932955592020*n^11*r^8+11347165196888290*n^10*r^9+314198164455357820*n^9*r^10-407422322557337175*n^8*r^11-7821198000*n^13*r^5+415128714660*n^12*r^6+69266194214580*n^11*r^7+4835495511914760*n^10*r^8+187778790700196080*n^9*r^9+3108982924590369970*n^8*r^10-8966152305654639920*n^7*r^11+3752892000*n^13*r^4+203475175200*n^12*r^5+12666629374344*n^11*r^6+634905045658620*n^10*r^7+20464073915319540*n^9*r^8+287281369381150870*n^8*r^9-2247742040192063580*n^7*r^10+28987149579961942380*n^6*r^11+42768534600*n^12*r^4+2114648192448*n^11*r^5+85623094145160*n^10*r^6+2217679304997420*n^9*r^7-5751862071719940*n^8*r^8-2828359203479940020*n^7*r^9-71073893153795780820*n^6*r^10+397337112180436670000*n^5*r^11-1634673150*n^12*r^3+107912966040*n^11*r^4+2682917781588*n^10*r^5-41099103254880*n^9*r^6-9612756688647420*n^8*r^7-558968956496521560*n^7*r^8-15783821377769337860*n^6*r^9-148446976399651497040*n^5*r^10-325026354207410191875*n^4*r^11-86605200*n^12*r^2-19966828860*n^11*r^3-529931445120*n^10*r^4-39397682408040*n^9*r^5-2204243660761560*n^8*r^6-94008116339173080*n^7*r^7-2603864291008689720*n^6*r^8-30460293953213899280*n^5*r^9+193931338668712521250*n^4*r^10-3924002923366713825000*n^3*r^11-17321040*n^12*r-1078234740*n^11*r^2-103394339730*n^10*r^3-3725874064440*n^9*r^4-175177689508800*n^8*r^5-6273760682657160*n^7*r^6-142401995117975340*n^6*r^7-10903523192931600*n^5*r^8+105640254110487223050*n^4*r^9+1997514615475135515000*n^3*r^10+640628369201426276250*n^2*r^11-184469076*n^11*r-5980089060*n^10*r^2-290836139220*n^9*r^3-8151711563160*n^8*r^4-190567235426040*n^7*r^5+1557466097843304*n^6*r^6+414449183674464840*n^5*r^7+20705832032882703300*n^4*r^8+487118881780418827500*n^3*r^9+3809265668637014055000*n^2*r^10+6823323752165242132500*n*r^11+4251528*n^11-853061220*n^10*r-18537843060*n^9*r^2-432880214580*n^8*r^3-3142487003040*n^7*r^4+403226655514848*n^6*r^5+32525434394081640*n^5*r^6+1372276729152237150*n^4*r^7+31969867785096354300*n^3*r^8+218450518635046818750*n^2*r^9-3599722772450754067500*n*r^10+46766808*n^10-2195441820*n^9*r-32775737940*n^8*r^2-105869083320*n^7*r^3+21340323821520*n^6*r^4+1442778530829768*n^5*r^5+54771613735055580*n^4*r^6+1127067701020064100*n^3*r^7-423138594646845000*n^2*r^8-523748935534422315000*n*r^9-5687785861922231572500*r^10+233834040*n^9-3234704220*n^8*r-25228094760*n^7*r^2+947901131100*n^6*r^3+52642647493920*n^5*r^4+1823577041678040*n^4*r^5+32863670278084800*n^3*r^6-221879162737306800*n^2*r^7-25772496086754202500*n*r^8-378338979474140107500*r^9+701502120*n^8-2052543240*n^7*r+21642639480*n^6*r^2+2189359248120*n^5*r^3+62690787763560*n^4*r^4+1119853637294040*n^3*r^5-2842529281471440*n^2*r^6-695729920991242500*n*r^7-12029753684545987500*r^8+1403004240*n^7+1709586648*n^6*r+82543416120*n^5*r^2+2612043865530*n^4*r^3+44546109216840*n^3*r^4+263902084484940*n^2*r^5-11097384698066040*n*r^6-244951807074232500*r^7+1964205936*n^6+5378182920*n^5*r+106498414440*n^4*r^2+1934545098420*n^3*r^3+19191579525360*n^2*r^4-38762554620240*n*r^5-3378853884285000*r^6+1964205936*n^5+6053703480*n^4*r+79377996060*n^3*r^2+896199991830*n^2*r^3+4631348751480*n*r^4-22401465581880*r^5+1403004240*n^4+3996829980*n^3*r+36023432940*n^2*r^2+239193458460*n*r^3+479593616040*r^4+701502120*n^3+1623847500*n^2*r+9297068220*n*r^2+28189992600*r^3+233834040*n^2+378464724*n*r+1052253180*r^2+46766808*n+38972340*r+4251528)/r^11 The limit of the standardized moment is, 0 Theorem, 12 Central moment, 12, of X_n is (1/292897224426269531250)*(8758750000000*n^18*F(n+1)^12+346058212500000*n^17*F(n+1)^12-4700306157421875*n^16*F(n+1)^12-161337432656400000*n^15*F(n+1)^12+4284604518468787500*n^14*F(n+1)^12+65487832402036873080*n^13*F(n+1)^12-760378147527860003324*n^12*F(n+1)^12-28726511814*F(n)^12*n^12-9358685530060660864980*n^11*F(n+1)^12-344718141768*F(n)^12*n^11+41412932188409712130200*n^10*F(n+1)^12-1895949779724*F(n)^12*n^10+414719617189601206733250*n^9*F(n+1)^12-6319832599080*F(n)^12*n^9-283312456490723991978075*n^8*F(n+1)^12-14219623347930*F(n)^12*n^8+2305704044507713689582600*n^7*F(n+1)^12-22751397356688*F(n)^12*n^7-24530668264238740010907500*n^6*F(n+1)^12-26543296916136*F(n)^12*n^6-418378076103018895494881250*n^5*F(n+1)^12-22751397356688*F(n)^12*n^5+383925858829972706067843750*n^4*F(n+1)^12-14219623347930*F(n)^12*n^4+5398927013462716323141825000*n^3*F(n+1)^12-6319832599080*F(n)^12*n^3-962969248194283088783943750*n^2*F(n+1)^12-1895949779724*F(n)^12*n^2-12162720170136279586949156250*n*F(n+1)^12-344718141768*F(n)^12*n+5684494442749684135093406250*F(n)*F(n+1)^11+419246695882287689208975000*F(n+1)^10*F(n)^2+13943683088519433661912500*F(n+1)^9*F(n)^3+295571048029294912875000*F(n+1)^8*F(n)^4+4513849424860419393750*F(n+1)^7*F(n)^5+49811063962129470000*F(n+1)^6*F(n)^6+275202004673395800*F(n+1)^5*F(n)^7-5050120776901200*F(n+1)^4*F(n)^8-259735544318250*F(n+1)^3*F(n)^9-8617953544200*F(n+1)^2*F(n)^10-287265118140*F(n+1)*F(n)^11-28726511814*F(n)^12-84264434654400*F(n+1)*F(n)^11*n^5-1068360762807351630648281250*F(n+1)^11*F(n)*n^4-175846897933297756959543750*F(n+1)^10*F(n)^2*n^4-21997980761128035490827000*F(n+1)^9*F(n)^3*n^4-1299520201103461435848750*F(n+1)^8*F(n)^4*n^4-46302484771375730147250*F(n+1)^7*F(n)^5*n^4-1300367842278681676500*F(n+1)^6*F(n)^6*n^4-36393302188056013200*F(n+1)^5*F(n)^7*n^4-1135204707722265180*F(n+1)^4*F(n)^8*n^4-42022944868094190*F(n+1)^3*F(n)^9*n^4-1529750590788420*F(n+1)^2*F(n)^10*n^4-74082482133660*F(n+1)*F(n)^11*n^4-2385074370259021571754487500*F(n+1)^11*F(n)*n^3-424929747383511181218225000*F(n+1)^10*F(n)^2*n^3-26021226112589327737162500*F(n+1)^9*F(n)^3*n^3-781178011963954478874000*F(n+1)^8*F(n)^4*n^3-16920178778108009804400*F(n+1)^7*F(n)^5*n^3-448918935557188496400*F(n+1)^6*F(n)^6*n^3-17139438849987253800*F(n+1)^5*F(n)^7*n^3-674130585252524400*F(n+1)^4*F(n)^8*n^3-26139242568298860*F(n+1)^3*F(n)^9*n^3-947623788050940*F(n+1)^2*F(n)^10*n^3-41430013705080*F(n+1)*F(n)^11*n^3-1124247045383002936640700000*F(n+1)^11*F(n)*n^2+2289772503838299015900000*F(n+1)^10*F(n)^2*n^2+11280911630347226383425000*F(n+1)^9*F(n)^3*n^2+639865399398199080356250*F(n+1)^8*F(n)^4*n^2+16792087544792922562200*F(n+1)^7*F(n)^5*n^2+203005333531576976400*F(n+1)^6*F(n)^6*n^2-2811707543759914800*F(n+1)^5*F(n)^7*n^2-251686189517612850*F(n+1)^4*F(n)^8*n^2-10475494913683800*F(n+1)^3*F(n)^9*n^2-371676377188116*F(n+1)^2*F(n)^10*n^2-14759043403104*F(n+1)*F(n)^11*n^2+5910947800168602702097350000*F(n+1)^11*F(n)*n+692939279466297852912787500*F(n+1)^10*F(n)^2*n+33254658807258250457550000*F(n+1)^9*F(n)^3*n+927874342489046358656250*F(n+1)^8*F(n)^4*n+17311443905427431760000*F(n+1)^7*F(n)^5*n+213001444392110173800*F(n+1)^6*F(n)^6*n+744997487066632800*F(n+1)^5*F(n)^7*n-53919316892791350*F(n+1)^4*F(n)^8*n-2465160291594000*F(n+1)^3*F(n)^9*n-84807046544220*F(n+1)^2*F(n)^10*n-3076928598744*F(n+1)*F(n)^11*n+85135050000000*F(n+1)^10*F(n)^2*n^17+405179775000000*F(n+1)^11*F(n)*n^17+56756700000000*F(n+1)^9*F(n)^3*n^17+5153429531250000*F(n+1)^11*F(n)*n^16-989694956250000*F(n+1)^10*F(n)^2*n^16-439864425000000*F(n+1)^9*F(n)^3*n^16-702364162500000*F(n+1)^8*F(n)^4*n^16-85454591947725000*F(n+1)^11*F(n)*n^15-87636366417600000*F(n+1)^10*F(n)^2*n^15-51904062960750000*F(n+1)^9*F(n)^3*n^15-6703746674625000*F(n+1)^8*F(n)^4*n^15+1877994067950000*F(n+1)^7*F(n)^5*n^15+64362097800000*F(n+1)^6*F(n)^6*n^15+18389170800000*F(n+1)^5*F(n)^7*n^15-2622072789748912500*F(n+1)^11*F(n)*n^14-1956394618265587500*F(n+1)^10*F(n)^2*n^14-329620984230037500*F(n+1)^9*F(n)^3*n^14+162071305833937500*F(n+1)^8*F(n)^4*n^14+27533760641887500*F(n+1)^7*F(n)^5*n^14+567190986862500*F(n+1)^6*F(n)^6*n^14+116245829700000*F(n+1)^5*F(n)^7*n^14-39897933075000*F(n+1)^4*F(n)^8*n^14-36767016945865540740*F(n+1)^11*F(n)*n^13-3529088364200981400*F(n+1)^10*F(n)^2*n^13+10511508898553808600*F(n+1)^9*F(n)^3*n^13+2246797102611461400*F(n+1)^8*F(n)^4*n^13+47552034781971720*F(n+1)^7*F(n)^5*n^13-6382296409048560*F(n+1)^6*F(n)^6*n^13-2381337197038800*F(n+1)^5*F(n)^7*n^13-494893961862300*F(n+1)^4*F(n)^8*n^13+15320806300800*F(n+1)^3*F(n)^9*n^13+702203622120*F(n+1)^2*F(n)^10*n^13+127673385840*F(n+1)*F(n)^11*n^13+65884953284048116764*F(n+1)^11*F(n)*n^12+432015179892349595724*F(n+1)^10*F(n)^2*n^12+116896592726152490160*F(n+1)^9*F(n)^3*n^12-1195313820892821630*F(n+1)^8*F(n)^4*n^12-1319153741111912706*F(n+1)^7*F(n)^5*n^12-195164726566213404*F(n+1)^6*F(n)^6*n^12-28407434376104784*F(n+1)^5*F(n)^7*n^12-1607503682764980*F(n+1)^4*F(n)^8*n^12+202250602343790*F(n+1)^3*F(n)^9*n^12+9428679544284*F(n+1)^2*F(n)^10*n^12+1487394945036*F(n+1)*F(n)^11*n^12+8642153141926483268544*F(n+1)^11*F(n)*n^11+3561165481150382653548*F(n+1)^10*F(n)^2*n^11-338141171679732095220*F(n+1)^9*F(n)^3*n^11-127841409895542262920*F(n+1)^8*F(n)^4*n^11-13130435739178157400*F(n+1)^7*F(n)^5*n^11-1446585205049888904*F(n+1)^6*F(n)^6*n^11-58681070895735288*F(n+1)^5*F(n)^7*n^11+4446417171956760*F(n+1)^4*F(n)^8*n^11+1153667353899060*F(n+1)^3*F(n)^9*n^11+57038085124020*F(n+1)^2*F(n)^10*n^11+7647635811816*F(n+1)*F(n)^11*n^11+48917650064208915029040*F(n+1)^11*F(n)*n^10-22044823032901671928926*F(n+1)^10*F(n)^2*n^10-7811340716479933252620*F(n+1)^9*F(n)^3*n^10-630690648215773525380*F(n+1)^8*F(n)^4*n^10-51751147853964719160*F(n+1)^7*F(n)^5*n^10-622758889305352800*F(n+1)^6*F(n)^6*n^10+454167716014748736*F(n+1)^5*F(n)^7*n^10+45084510102742110*F(n+1)^4*F(n)^8*n^10+3682121726523240*F(n+1)^3*F(n)^9*n^10+197670319626780*F(n+1)^2*F(n)^10*n^10+22470515907840*F(n+1)*F(n)^11*n^10-557086416268665030998250*F(n+1)^11*F(n)*n^9-286869915945680219252100*F(n+1)^10*F(n)^2*n^9-17780434105103012282940*F(n+1)^9*F(n)^3*n^9-253237623057338839920*F(n+1)^8*F(n)^4*n^9+140421989858205395340*F(n+1)^7*F(n)^5*n^9+33289691077966443120*F(n+1)^6*F(n)^6*n^9+2651780478100113360*F(n+1)^5*F(n)^7*n^9+125902114441273170*F(n+1)^4*F(n)^8*n^9+6751879336762560*F(n+1)^3*F(n)^9*n^9+411842424373380*F(n+1)^2*F(n)^10*n^9+40025606460840*F(n+1)*F(n)^11*n^9-4698529037248239990997200*F(n+1)^11*F(n)*n^8-45614335144612050466650*F(n+1)^10*F(n)^2*n^8+104803884279543021873300*F(n+1)^9*F(n)^3*n^8+14236153843032892690920*F(n+1)^8*F(n)^4*n^8+1918294092021426709590*F(n+1)^7*F(n)^5*n^8+125607671441841869280*F(n+1)^6*F(n)^6*n^8+4524668901799005960*F(n+1)^5*F(n)^7*n^8+119679542363581200*F(n+1)^4*F(n)^8*n^8+5030379279615690*F(n+1)^3*F(n)^9*n^8+459241168866480*F(n+1)^2*F(n)^10*n^8+38972301027660*F(n+1)*F(n)^11*n^8+9872947230572686227953700*F(n+1)^11*F(n)*n^7+6466707841673489904093600*F(n+1)^10*F(n)^2*n^7+710029529398955235670200*F(n+1)^9*F(n)^3*n^7+77785214356744271477100*F(n+1)^8*F(n)^4*n^7+4367547564913685696544*F(n+1)^7*F(n)^5*n^7+70226305756296665976*F(n+1)^6*F(n)^6*n^7-2608479984037191264*F(n+1)^5*F(n)^7*n^7-193050819901419480*F(n+1)^4*F(n)^8*n^7-7788268046318760*F(n+1)^3*F(n)^9*n^7+8005121292168*F(n+1)^2*F(n)^10*n^7+2527933039632*F(n+1)*F(n)^11*n^7+136704915368811230867325900*F(n+1)^11*F(n)*n^6+17409610428666047934492150*F(n+1)^10*F(n)^2*n^6+1657808363737579144291200*F(n+1)^9*F(n)^3*n^6+63050136303553693544250*F(n+1)^8*F(n)^4*n^6-5031133671596963750820*F(n+1)^7*F(n)^5*n^6-503931149995418829684*F(n+1)^6*F(n)^6*n^6-22781357788482781488*F(n+1)^5*F(n)^7*n^6-784198843211723940*F(n+1)^4*F(n)^8*n^6-29050929887419440*F(n+1)^3*F(n)^9*n^6-874243509539400*F(n+1)^2*F(n)^10*n^6-52243949485728*F(n+1)*F(n)^11*n^6+88744105784029971441416250*F(n+1)^11*F(n)*n^5-11160975776243691588290100*F(n+1)^10*F(n)^2*n^5-2943822676881543219863100*F(n+1)^9*F(n)^3*n^5-511531894064715058284750*F(n+1)^8*F(n)^4*n^5-33048583825513344788700*F(n+1)^7*F(n)^5*n^5-1292837882293260543240*F(n+1)^6*F(n)^6*n^5-40348435198578290784*F(n+1)^5*F(n)^7*n^5-1221776125982652240*F(n+1)^4*F(n)^8*n^5-44422550195783760*F(n+1)^3*F(n)^9*n^5-1563105262839120*F(n+1)^2*F(n)^10*n^5)/F(n+1)^12 which is asymptotic to (1/292897224426269531250)*(8758750000000*n^18*r^12+346058212500000*n^17*r^12+405179775000000*n^17*r^11-4700306157421875*n^16*r^12+85135050000000*n^17*r^10+5153429531250000*n^16*r^11-161337432656400000*n^15*r^12+56756700000000*n^17*r^9-989694956250000*n^16*r^10-85454591947725000*n^15*r^11+4284604518468787500*n^14*r^12-439864425000000*n^16*r^9-87636366417600000*n^15*r^10-2622072789748912500*n^14*r^11+65487832402036873080*n^13*r^12-702364162500000*n^16*r^8-51904062960750000*n^15*r^9-1956394618265587500*n^14*r^10-36767016945865540740*n^13*r^11-760378147527860003324*n^12*r^12-6703746674625000*n^15*r^8-329620984230037500*n^14*r^9-3529088364200981400*n^13*r^10+65884953284048116764*n^12*r^11-9358685530060660864980*n^11*r^12+1877994067950000*n^15*r^7+162071305833937500*n^14*r^8+10511508898553808600*n^13*r^9+432015179892349595724*n^12*r^10+8642153141926483268544*n^11*r^11+41412932188409712130200*n^10*r^12+64362097800000*n^15*r^6+27533760641887500*n^14*r^7+2246797102611461400*n^13*r^8+116896592726152490160*n^12*r^9+3561165481150382653548*n^11*r^10+48917650064208915029040*n^10*r^11+414719617189601206733250*n^9*r^12+18389170800000*n^15*r^5+567190986862500*n^14*r^6+47552034781971720*n^13*r^7-1195313820892821630*n^12*r^8-338141171679732095220*n^11*r^9-22044823032901671928926*n^10*r^10-557086416268665030998250*n^9*r^11-283312456490723991978075*n^8*r^12+116245829700000*n^14*r^5-6382296409048560*n^13*r^6-1319153741111912706*n^12*r^7-127841409895542262920*n^11*r^8-7811340716479933252620*n^10*r^9-286869915945680219252100*n^9*r^10-4698529037248239990997200*n^8*r^11+2305704044507713689582600*n^7*r^12-39897933075000*n^14*r^4-2381337197038800*n^13*r^5-195164726566213404*n^12*r^6-13130435739178157400*n^11*r^7-630690648215773525380*n^10*r^8-17780434105103012282940*n^9*r^9-45614335144612050466650*n^8*r^10+9872947230572686227953700*n^7*r^11-24530668264238740010907500*n^6*r^12-494893961862300*n^13*r^4-28407434376104784*n^12*r^5-1446585205049888904*n^11*r^6-51751147853964719160*n^10*r^7-253237623057338839920*n^9*r^8+104803884279543021873300*n^8*r^9+6466707841673489904093600*n^7*r^10+136704915368811230867325900*n^6*r^11-418378076103018895494881250*n^5*r^12+15320806300800*n^13*r^3-1607503682764980*n^12*r^4-58681070895735288*n^11*r^5-622758889305352800*n^10*r^6+140421989858205395340*n^9*r^7+14236153843032892690920*n^8*r^8+710029529398955235670200*n^7*r^9+17409610428666047934492150*n^6*r^10+88744105784029971441416250*n^5*r^11+383925858829972706067843750*n^4*r^12+702203622120*n^13*r^2+202250602343790*n^12*r^3+4446417171956760*n^11*r^4+454167716014748736*n^10*r^5+33289691077966443120*n^9*r^6+1918294092021426709590*n^8*r^7+77785214356744271477100*n^7*r^8+1657808363737579144291200*n^6*r^9-11160975776243691588290100*n^5*r^10-1068360762807351630648281250*n^4*r^11+5398927013462716323141825000*n^3*r^12+127673385840*n^13*r+9428679544284*n^12*r^2+1153667353899060*n^11*r^3+45084510102742110*n^10*r^4+2651780478100113360*n^9*r^5+125607671441841869280*n^8*r^6+4367547564913685696544*n^7*r^7+63050136303553693544250*n^6*r^8-2943822676881543219863100*n^5*r^9-175846897933297756959543750*n^4*r^10-2385074370259021571754487500*n^3*r^11-962969248194283088783943750*n^2*r^12+1487394945036*n^12*r+57038085124020*n^11*r^2+3682121726523240*n^10*r^3+125902114441273170*n^9*r^4+4524668901799005960*n^8*r^5+70226305756296665976*n^7*r^6-5031133671596963750820*n^6*r^7-511531894064715058284750*n^5*r^8-21997980761128035490827000*n^4*r^9-424929747383511181218225000*n^3*r^10-1124247045383002936640700000*n^2*r^11-12162720170136279586949156250*n*r^12-28726511814*n^12+7647635811816*n^11*r+197670319626780*n^10*r^2+6751879336762560*n^9*r^3+119679542363581200*n^8*r^4-2608479984037191264*n^7*r^5-503931149995418829684*n^6*r^6-33048583825513344788700*n^5*r^7-1299520201103461435848750*n^4*r^8-26021226112589327737162500*n^3*r^9+2289772503838299015900000*n^2*r^10+5910947800168602702097350000*n*r^11-344718141768*n^11+22470515907840*n^10*r+411842424373380*n^9*r^2+5030379279615690*n^8*r^3-193050819901419480*n^7*r^4-22781357788482781488*n^6*r^5-1292837882293260543240*n^5*r^6-46302484771375730147250*n^4*r^7-781178011963954478874000*n^3*r^8+11280911630347226383425000*n^2*r^9+692939279466297852912787500*n*r^10+5684494442749684135093406250*r^11-1895949779724*n^10+40025606460840*n^9*r+459241168866480*n^8*r^2-7788268046318760*n^7*r^3-784198843211723940*n^6*r^4-40348435198578290784*n^5*r^5-1300367842278681676500*n^4*r^6-16920178778108009804400*n^3*r^7+639865399398199080356250*n^2*r^8+33254658807258250457550000*n*r^9+419246695882287689208975000*r^10-6319832599080*n^9+38972301027660*n^8*r+8005121292168*n^7*r^2-29050929887419440*n^6*r^3-1221776125982652240*n^5*r^4-36393302188056013200*n^4*r^5-448918935557188496400*n^3*r^6+16792087544792922562200*n^2*r^7+927874342489046358656250*n*r^8+13943683088519433661912500*r^9-14219623347930*n^8+2527933039632*n^7*r-874243509539400*n^6*r^2-44422550195783760*n^5*r^3-1135204707722265180*n^4*r^4-17139438849987253800*n^3*r^5+203005333531576976400*n^2*r^6+17311443905427431760000*n*r^7+295571048029294912875000*r^8-22751397356688*n^7-52243949485728*n^6*r-1563105262839120*n^5*r^2-42022944868094190*n^4*r^3-674130585252524400*n^3*r^4-2811707543759914800*n^2*r^5+213001444392110173800*n*r^6+4513849424860419393750*r^7-26543296916136*n^6-84264434654400*n^5*r-1529750590788420*n^4*r^2-26139242568298860*n^3*r^3-251686189517612850*n^2*r^4+744997487066632800*n*r^5+49811063962129470000*r^6-22751397356688*n^5-74082482133660*n^4*r-947623788050940*n^3*r^2-10475494913683800*n^2*r^3-53919316892791350*n*r^4+275202004673395800*r^5-14219623347930*n^4-41430013705080*n^3*r-371676377188116*n^2*r^2-2465160291594000*n*r^3-5050120776901200*r^4-6319832599080*n^3-14759043403104*n^2*r-84807046544220*n*r^2-259735544318250*r^3-1895949779724*n^2-3076928598744*n*r-8617953544200*r^2-344718141768*n-287265118140*r-28726511814)/r^12 The limit of the standardized moment is, 10395 Theorem, 13 Central moment, 13, of X_n is -(1/62584877014160156250)*(-2191533012396*F(n+1)^2*F(n)^11*n^12-276819113844*F(n+1)*F(n)^12*n^12-51785375414145711426270*F(n+1)^12*F(n)*n^11-17459835272738098291688*F(n+1)^11*F(n)^2*n^11+3180564213537816751464*F(n+1)^10*F(n)^3*n^11+932966432965405451340*F(n+1)^9*F(n)^4*n^11+63968114334486021660*F(n+1)^8*F(n)^5*n^11+4296082015039094280*F(n+1)^7*F(n)^6*n^11+113534367008870808*F(n+1)^6*F(n)^7*n^11-18953549517836934*F(n+1)^5*F(n)^8*n^11-2072650139780220*F(n+1)^4*F(n)^9*n^11-181083418916400*F(n+1)^3*F(n)^10*n^11-8383885670160*F(n+1)^2*F(n)^11*n^11-912671264232*F(n+1)*F(n)^12*n^11-178667686578060448308540*F(n+1)^12*F(n)*n^10+177289672516873230609295*F(n+1)^11*F(n)^2*n^10+53510796532490197939038*F(n+1)^10*F(n)^3*n^10+2884899731131319461560*F(n+1)^9*F(n)^4*n^10+68702629545195535890*F(n+1)^8*F(n)^5*n^10-6132013984226910780*F(n+1)^7*F(n)^6*n^10-1823657416641300240*F(n+1)^6*F(n)^7*n^10-148575468767869143*F(n+1)^5*F(n)^8*n^10-7160156166593430*F(n+1)^4*F(n)^9*n^10-390400585544970*F(n+1)^3*F(n)^10*n^10-20002163781600*F(n+1)^2*F(n)^11*n^10-1893821889960*F(n+1)*F(n)^12*n^10+4192093720127650736348950*F(n+1)^12*F(n)*n^9+1873367343475407982902700*F(n+1)^11*F(n)^2*n^9+56340681149922739970400*F(n+1)^10*F(n)^3*n^9-10273737174855955360560*F(n+1)^9*F(n)^4*n^9-1188703255968851272650*F(n+1)^8*F(n)^5*n^9-137824167932964783270*F(n+1)^7*F(n)^6*n^9-8859924086894080200*F(n+1)^6*F(n)^7*n^9-343421918081252010*F(n+1)^5*F(n)^8*n^9-10283862481262370*F(n+1)^4*F(n)^9*n^9-440830784844450*F(n+1)^3*F(n)^10*n^9-28375410002940*F(n+1)^2*F(n)^11*n^9-2393875984500*F(n+1)*F(n)^12*n^9+29480366381833655769488150*F(n+1)^12*F(n)*n^8-1855609651648763151094525*F(n+1)^11*F(n)^2*n^8-1130184353419759253766150*F(n+1)^10*F(n)^3*n^8-92494272340991209013325*F(n+1)^9*F(n)^4*n^8-7690215589799051815506*F(n+1)^8*F(n)^5*n^8-419941474477378499646*F(n+1)^7*F(n)^6*n^8-10932190098235232112*F(n+1)^6*F(n)^7*n^8-92516144562288018*F(n+1)^5*F(n)^8*n^8+3079042893656730*F(n+1)^4*F(n)^9*n^8+101063060396298*F(n+1)^3*F(n)^10*n^8-14561149655052*F(n+1)^2*F(n)^11*n^8-1257582850524*F(n+1)*F(n)^12*n^8-106501231231458147623303050*F(n+1)^12*F(n)*n^7-54342639040369334528902600*F(n+1)^11*F(n)^2*n^7-4106658447579150471808800*F(n+1)^10*F(n)^3*n^7-261846382975792988823450*F(n+1)^9*F(n)^4*n^7-11680263850399551487080*F(n+1)^8*F(n)^5*n^7+803538792*F(n)^13+389019881250000*F(n+1)^10*F(n)^3*n^17+35472937500000*F(n+1)^9*F(n)^4*n^17+59594535000000*F(n+1)^8*F(n)^5*n^17-91400520354893750*F(n+1)^12*F(n)*n^16+60027185743525000*F(n+1)^11*F(n)^2*n^16+17223481312537500*F(n+1)^10*F(n)^3*n^16+5598560561343750*F(n+1)^9*F(n)^4*n^16+639193955400000*F(n+1)^8*F(n)^5*n^16-128724195600000*F(n+1)^7*F(n)^6*n^16-3502699200000*F(n+1)^6*F(n)^7*n^16-875674800000*F(n+1)^5*F(n)^8*n^16+2232271478052070000*F(n+1)^12*F(n)*n^15+1386454700853722500*F(n+1)^11*F(n)^2*n^15+309397736390242500*F(n+1)^10*F(n)^3*n^15+41506795632802500*F(n+1)^9*F(n)^4*n^15-13073837534257500*F(n+1)^8*F(n)^5*n^15-2008672112947500*F(n+1)^7*F(n)^6*n^15-31447671255000*F(n+1)^6*F(n)^7*n^15-6474520552500*F(n+1)^5*F(n)^8*n^15+1674728055000*F(n+1)^4*F(n)^9*n^15+34807359702898499380*F(n+1)^12*F(n)*n^14+8375354178572160430*F(n+1)^11*F(n)^2*n^14+559247819004119700*F(n+1)^10*F(n)^3*n^14-1141932488091472350*F(n+1)^9*F(n)^4*n^14-204529229305971570*F(n+1)^8*F(n)^5*n^14-4946567393697930*F(n+1)^7*F(n)^6*n^14+360488675881620*F(n+1)^6*F(n)^7*n^14+107002738170900*F(n+1)^5*F(n)^8*n^14+22458103217550*F(n+1)^4*F(n)^9*n^14-575121316770*F(n+1)^3*F(n)^10*n^14-23213342880*F(n+1)^2*F(n)^11*n^14-3868890480*F(n+1)*F(n)^12*n^14+69982409400934470216*F(n+1)^12*F(n)*n^13-75628902934663278368*F(n+1)^11*F(n)^2*n^13-71678285206521532812*F(n+1)^10*F(n)^3*n^13-14407517658820628160*F(n+1)^9*F(n)^4*n^13-79605847452937806*F(n+1)^8*F(n)^5*n^13+87894528298410834*F(n+1)^7*F(n)^6*n^13+11322721981699128*F(n+1)^6*F(n)^7*n^13+1462811154376572*F(n+1)^5*F(n)^8*n^13+88437659940630*F(n+1)^4*F(n)^9*n^13-8161284757626*F(n+1)^3*F(n)^10*n^13-334465581996*F(n+1)^2*F(n)^11*n^13-48941464572*F(n+1)*F(n)^12*n^13-2796888989362053980394*F(n+1)^12*F(n)*n^12-2795555048421843309056*F(n+1)^11*F(n)^2*n^12-671233625581443351336*F(n+1)^10*F(n)^3*n^12+25557073094943293085*F(n+1)^9*F(n)^4*n^12+11067818891971932090*F(n+1)^8*F(n)^5*n^12+973182206671739064*F(n+1)^7*F(n)^6*n^12+91204819603413516*F(n+1)^6*F(n)^7*n^12+4135366740656151*F(n+1)^5*F(n)^8*n^12-117696144195630*F(n+1)^4*F(n)^9*n^12-50819721342390*F(n+1)^3*F(n)^10*n^12-21953442516334271929882293750*F(n+1)^12*F(n)*n^2-1771086102368206109484806250*F(n+1)^11*F(n)^2*n^2-117321075184377836659387500*F(n+1)^10*F(n)^3*n^2-4950471558352743251521875*F(n+1)^9*F(n)^4*n^2-130410564534822588266250*F(n+1)^8*F(n)^5*n^2-2267341097387400134100*F(n+1)^7*F(n)^6*n^2-22996243886884468200*F(n+1)^6*F(n)^7*n^2+100281583193316525*F(n+1)^5*F(n)^8*n^2+12763761561901350*F(n+1)^4*F(n)^9*n^2+479752252949970*F(n+1)^3*F(n)^10*n^2+15231048041664*F(n+1)^2*F(n)^11*n^2+540484000056*F(n+1)*F(n)^12*n^2-41328476219615140909237406250*F(n+1)^12*F(n)*n-3948971946601445611994681250*F(n+1)^11*F(n)^2*n-185828608004023428208537500*F(n+1)^10*F(n)^3*n-5244716249509613923068750*F(n+1)^9*F(n)^4*n-101907435823605140478750*F(n+1)^8*F(n)^5*n-1453998726974785241250*F(n+1)^7*F(n)^6*n-14584533607421692200*F(n+1)^6*F(n)^7*n-48352267423939050*F(n+1)^5*F(n)^8*n+2460336089661450*F(n+1)^4*F(n)^9*n+100968172274970*F(n+1)^3*F(n)^10*n+3115424059020*F(n+1)^2*F(n)^11*n+101945264148*F(n+1)*F(n)^12*n+44545023487114994844*F(n+1)^7*F(n)^6*n^7+24125758805208791016*F(n+1)^6*F(n)^7*n^7+1212580718303999616*F(n+1)^5*F(n)^8*n^7+40932163158606720*F(n+1)^4*F(n)^9*n^7+1369599696344880*F(n+1)^3*F(n)^10*n^7+30028780349568*F(n+1)^2*F(n)^11*n^7+1506545952912*F(n+1)*F(n)^12*n^7-1070432288657643566153248750*F(n+1)^12*F(n)*n^6-81275404935038861339767975*F(n+1)^11*F(n)^2*n^6-675905980986517479348150*F(n+1)^10*F(n)^3*n^6+155089576575498393553725*F(n+1)^9*F(n)^4*n^6+37586090287080989223570*F(n+1)^8*F(n)^5*n^6+2544944551868311562970*F(n+1)^7*F(n)^6*n^6+100113590274648098148*F(n+1)^6*F(n)^7*n^6+3017767799308588326*F(n+1)^5*F(n)^8*n^6+83986514715833730*F(n+1)^4*F(n)^9*n^6+2730976871993370*F(n+1)^3*F(n)^10*n^6+82221660480960*F(n+1)^2*F(n)^11*n^6+4136617701216*F(n+1)*F(n)^12*n^6+265163316651958665948052500*F(n+1)^12*F(n)*n^5+377849872687740036332498750*F(n+1)^11*F(n)^2*n^5+32397075623076125963601600*F(n+1)^10*F(n)^3*n^5+2789361940509615849528150*F(n+1)^9*F(n)^4*n^5+151337795788549042422750*F(n+1)^8*F(n)^5*n^5+5306493788738158005990*F(n+1)^7*F(n)^6*n^5+144636559465524005880*F(n+1)^6*F(n)^7*n^5+3670601064382724472*F(n+1)^5*F(n)^8*n^5+98639046990854370*F(n+1)^4*F(n)^9*n^5+3211031167073730*F(n+1)^3*F(n)^10*n^5+103702707648540*F(n+1)^2*F(n)^11*n^5+4798391417820*F(n+1)*F(n)^12*n^5+11856166283061954359965550000*F(n+1)^12*F(n)*n^4+1243680625428376405217959375*F(n+1)^11*F(n)^2*n^4+100753184735854787175243750*F(n+1)^10*F(n)^3*n^4+5344873467532264488800250*F(n+1)^9*F(n)^4*n^4+173959174372134294193050*F(n+1)^8*F(n)^5*n^4+4236427893222389264400*F(n+1)^7*F(n)^6*n^4+97769732115567411900*F(n+1)^6*F(n)^7*n^4+2562508719840744675*F(n+1)^5*F(n)^8*n^4+75679759138813830*F(n+1)^4*F(n)^9*n^4+2530133632296270*F(n+1)^3*F(n)^10*n^4+82849387961340*F(n+1)^2*F(n)^11*n^4+3500378661780*F(n+1)*F(n)^12*n^4+11670813452787310869880787500*F(n+1)^12*F(n)*n^3+1118415409800939205599962500*F(n+1)^11*F(n)^2*n^3+69283150994383097795887500*F(n+1)^10*F(n)^3*n^3+1637164241624488976831250*F(n+1)^9*F(n)^4*n^3+12267862071068017814400*F(n+1)^8*F(n)^5*n^3+24404785977335563800*F(n+1)^7*F(n)^6*n^3+14012825245068850200*F(n+1)^6*F(n)^7*n^3+956692741153599450*F(n+1)^5*F(n)^8*n^3+38698959795596100*F(n+1)^4*F(n)^9*n^3+1358226677231424*F(n+1)^3*F(n)^10*n^3+44058151008144*F(n+1)^2*F(n)^11*n^3+1702698700248*F(n+1)*F(n)^12*n^3+8758750000000*F(n+1)^12*F(n)*n^19-40377837500000*F(n+1)^12*F(n)*n^18-213100387500000*F(n+1)^11*F(n)^2*n^18-12612600000000*F(n+1)^10*F(n)^3*n^18-6306300000000*F(n+1)^9*F(n)^4*n^18-10654043400000000*F(n+1)^12*F(n)*n^17-3060723290625000*F(n+1)^11*F(n)^2*n^17+4379375000000*n^19*F(n+1)^13+341744528125000*n^18*F(n+1)^13+1063565940937500*n^17*F(n+1)^13-44301740110753125*n^16*F(n+1)^13+532850329148865000*n^15*F(n+1)^13-22998136785744269280*n^14*F(n+1)^13-466220381775019951184*n^13*F(n+1)^13+803538792*F(n)^13*n^13+5323830238624049352655*n^12*F(n+1)^13+10446004296*F(n)^13*n^12+78439568773988724623230*n^11*F(n+1)^13+62676025776*F(n)^13*n^11-359719261803502781555375*n^10*F(n+1)^13+229812094512*F(n)^13*n^10-4535369895009965008347350*n^9*F(n+1)^13+574530236280*F(n)^13*n^9+7158313249120434946351950*n^8*F(n+1)^13+1034154425304*F(n)^13*n^8+63504506220859612397238750*n^7*F(n+1)^13+1378872567072*F(n)^13*n^7+50788140455416355070454375*n^6*F(n+1)^13+1378872567072*F(n)^13*n^6+1495001053752757069089593750*n^5*F(n+1)^13+1034154425304*F(n)^13*n^5-1886430661499038156471571875*n^4*F(n+1)^13+574530236280*F(n)^13*n^4-31309354932624741734618106250*n^3*F(n+1)^13+229812094512*F(n)^13*n^3+6138459082869541592142046875*n^2*F(n+1)^13+62676025776*F(n)^13*n^2+89624258124262713937084781250*n*F(n+1)^13+10446004296*F(n)^13*n-18356450715450804323573718750*F(n)*F(n+1)^12-1894831480916561378364468750*F(n+1)^11*F(n)^2-69874449313714614868162500*F(n+1)^10*F(n)^3-1549298120946603740212500*F(n+1)^9*F(n)^4-24630920669107909406250*F(n+1)^8*F(n)^5-300923294990694626250*F(n+1)^7*F(n)^6-2767281331229415000*F(n+1)^6*F(n)^7-13104857365399800*F(n+1)^5*F(n)^8+210421699037550*F(n+1)^4*F(n)^9+9619834974750*F(n+1)^3*F(n)^10+287265118140*F(n+1)^2*F(n)^11+8705003580*F(n+1)*F(n)^12)/F(n+1)^13 which is asymptotic to -(1/62584877014160156250)*(4379375000000*n^19*r^13+8758750000000*n^19*r^12+341744528125000*n^18*r^13-40377837500000*n^18*r^12+1063565940937500*n^17*r^13-213100387500000*n^18*r^11-10654043400000000*n^17*r^12-44301740110753125*n^16*r^13-12612600000000*n^18*r^10-3060723290625000*n^17*r^11-91400520354893750*n^16*r^12+532850329148865000*n^15*r^13-6306300000000*n^18*r^9+389019881250000*n^17*r^10+60027185743525000*n^16*r^11+2232271478052070000*n^15*r^12-22998136785744269280*n^14*r^13+35472937500000*n^17*r^9+17223481312537500*n^16*r^10+1386454700853722500*n^15*r^11+34807359702898499380*n^14*r^12-466220381775019951184*n^13*r^13+59594535000000*n^17*r^8+5598560561343750*n^16*r^9+309397736390242500*n^15*r^10+8375354178572160430*n^14*r^11+69982409400934470216*n^13*r^12+5323830238624049352655*n^12*r^13+639193955400000*n^16*r^8+41506795632802500*n^15*r^9+559247819004119700*n^14*r^10-75628902934663278368*n^13*r^11-2796888989362053980394*n^12*r^12+78439568773988724623230*n^11*r^13-128724195600000*n^16*r^7-13073837534257500*n^15*r^8-1141932488091472350*n^14*r^9-71678285206521532812*n^13*r^10-2795555048421843309056*n^12*r^11-51785375414145711426270*n^11*r^12-359719261803502781555375*n^10*r^13-3502699200000*n^16*r^6-2008672112947500*n^15*r^7-204529229305971570*n^14*r^8-14407517658820628160*n^13*r^9-671233625581443351336*n^12*r^10-17459835272738098291688*n^11*r^11-178667686578060448308540*n^10*r^12-4535369895009965008347350*n^9*r^13-875674800000*n^16*r^5-31447671255000*n^15*r^6-4946567393697930*n^14*r^7-79605847452937806*n^13*r^8+25557073094943293085*n^12*r^9+3180564213537816751464*n^11*r^10+177289672516873230609295*n^10*r^11+4192093720127650736348950*n^9*r^12+7158313249120434946351950*n^8*r^13-6474520552500*n^15*r^5+360488675881620*n^14*r^6+87894528298410834*n^13*r^7+11067818891971932090*n^12*r^8+932966432965405451340*n^11*r^9+53510796532490197939038*n^10*r^10+1873367343475407982902700*n^9*r^11+29480366381833655769488150*n^8*r^12+63504506220859612397238750*n^7*r^13+1674728055000*n^15*r^4+107002738170900*n^14*r^5+11322721981699128*n^13*r^6+973182206671739064*n^12*r^7+63968114334486021660*n^11*r^8+2884899731131319461560*n^10*r^9+56340681149922739970400*n^9*r^10-1855609651648763151094525*n^8*r^11-106501231231458147623303050*n^7*r^12+50788140455416355070454375*n^6*r^13+22458103217550*n^14*r^4+1462811154376572*n^13*r^5+91204819603413516*n^12*r^6+4296082015039094280*n^11*r^7+68702629545195535890*n^10*r^8-10273737174855955360560*n^9*r^9-1130184353419759253766150*n^8*r^10-54342639040369334528902600*n^7*r^11-1070432288657643566153248750*n^6*r^12+1495001053752757069089593750*n^5*r^13-575121316770*n^14*r^3+88437659940630*n^13*r^4+4135366740656151*n^12*r^5+113534367008870808*n^11*r^6-6132013984226910780*n^10*r^7-1188703255968851272650*n^9*r^8-92494272340991209013325*n^8*r^9-4106658447579150471808800*n^7*r^10-81275404935038861339767975*n^6*r^11+265163316651958665948052500*n^5*r^12-1886430661499038156471571875*n^4*r^13-23213342880*n^14*r^2-8161284757626*n^13*r^3-117696144195630*n^12*r^4-18953549517836934*n^11*r^5-1823657416641300240*n^10*r^6-137824167932964783270*n^9*r^7-7690215589799051815506*n^8*r^8-261846382975792988823450*n^7*r^9-675905980986517479348150*n^6*r^10+377849872687740036332498750*n^5*r^11+11856166283061954359965550000*n^4*r^12-31309354932624741734618106250*n^3*r^13-3868890480*n^14*r-334465581996*n^13*r^2-50819721342390*n^12*r^3-2072650139780220*n^11*r^4-148575468767869143*n^10*r^5-8859924086894080200*n^9*r^6-419941474477378499646*n^8*r^7-11680263850399551487080*n^7*r^8+155089576575498393553725*n^6*r^9+32397075623076125963601600*n^5*r^10+1243680625428376405217959375*n^4*r^11+11670813452787310869880787500*n^3*r^12+6138459082869541592142046875*n^2*r^13-48941464572*n^13*r-2191533012396*n^12*r^2-181083418916400*n^11*r^3-7160156166593430*n^10*r^4-343421918081252010*n^9*r^5-10932190098235232112*n^8*r^6+44545023487114994844*n^7*r^7+37586090287080989223570*n^6*r^8+2789361940509615849528150*n^5*r^9+100753184735854787175243750*n^4*r^10+1118415409800939205599962500*n^3*r^11-21953442516334271929882293750*n^2*r^12+89624258124262713937084781250*n*r^13+803538792*n^13-276819113844*n^12*r-8383885670160*n^11*r^2-390400585544970*n^10*r^3-10283862481262370*n^9*r^4-92516144562288018*n^8*r^5+24125758805208791016*n^7*r^6+2544944551868311562970*n^6*r^7+151337795788549042422750*n^5*r^8+5344873467532264488800250*n^4*r^9+69283150994383097795887500*n^3*r^10-1771086102368206109484806250*n^2*r^11-41328476219615140909237406250*n*r^12+10446004296*n^12-912671264232*n^11*r-20002163781600*n^10*r^2-440830784844450*n^9*r^3+3079042893656730*n^8*r^4+1212580718303999616*n^7*r^5+100113590274648098148*n^6*r^6+5306493788738158005990*n^5*r^7+173959174372134294193050*n^4*r^8+1637164241624488976831250*n^3*r^9-117321075184377836659387500*n^2*r^10-3948971946601445611994681250*n*r^11-18356450715450804323573718750*r^12+62676025776*n^11-1893821889960*n^10*r-28375410002940*n^9*r^2+101063060396298*n^8*r^3+40932163158606720*n^7*r^4+3017767799308588326*n^6*r^5+144636559465524005880*n^5*r^6+4236427893222389264400*n^4*r^7+12267862071068017814400*n^3*r^8-4950471558352743251521875*n^2*r^9-185828608004023428208537500*n*r^10-1894831480916561378364468750*r^11+229812094512*n^10-2393875984500*n^9*r-14561149655052*n^8*r^2+1369599696344880*n^7*r^3+83986514715833730*n^6*r^4+3670601064382724472*n^5*r^5+97769732115567411900*n^4*r^6+24404785977335563800*n^3*r^7-130410564534822588266250*n^2*r^8-5244716249509613923068750*n*r^9-69874449313714614868162500*r^10+574530236280*n^9-1257582850524*n^8*r+30028780349568*n^7*r^2+2730976871993370*n^6*r^3+98639046990854370*n^5*r^4+2562508719840744675*n^4*r^5+14012825245068850200*n^3*r^6-2267341097387400134100*n^2*r^7-101907435823605140478750*n*r^8-1549298120946603740212500*r^9+1034154425304*n^8+1506545952912*n^7*r+82221660480960*n^6*r^2+3211031167073730*n^5*r^3+75679759138813830*n^4*r^4+956692741153599450*n^3*r^5-22996243886884468200*n^2*r^6-1453998726974785241250*n*r^7-24630920669107909406250*r^8+1378872567072*n^7+4136617701216*n^6*r+103702707648540*n^5*r^2+2530133632296270*n^4*r^3+38698959795596100*n^3*r^4+100281583193316525*n^2*r^5-14584533607421692200*n*r^6-300923294990694626250*r^7+1378872567072*n^6+4798391417820*n^5*r+82849387961340*n^4*r^2+1358226677231424*n^3*r^3+12763761561901350*n^2*r^4-48352267423939050*n*r^5-2767281331229415000*r^6+1034154425304*n^5+3500378661780*n^4*r+44058151008144*n^3*r^2+479752252949970*n^2*r^3+2460336089661450*n*r^4-13104857365399800*r^5+574530236280*n^4+1702698700248*n^3*r+15231048041664*n^2*r^2+100968172274970*n*r^3+210421699037550*r^4+229812094512*n^3+540484000056*n^2*r+3115424059020*n*r^2+9619834974750*r^3+62676025776*n^2+101945264148*n*r+287265118140*r^2+10446004296*n+8705003580*r+803538792)/r^13 The limit of the standardized moment is, 0 Theorem, 14 Central moment, 14, of X_n is (1/12069940567016601562500)*(14269881735367778520*F(n+1)^8*F(n)^6*n^15+375148471128528240*F(n+1)^7*F(n)^7*n^15-16655470438103640*F(n+1)^6*F(n)^8*n^15-4042347118266600*F(n+1)^5*F(n)^9*n^15-874179672846480*F(n+1)^4*F(n)^10*n^15+18837627747120*F(n+1)^3*F(n)^11*n^15+678990279240*F(n+1)^2*F(n)^12*n^15+104460042960*F(n+1)*F(n)^13*n^15-378313758212133261705036*F(n+1)^13*F(n)*n^14-195519766554738787248*F(n+1)^12*F(n)^2*n^14+14711647292469455264496*F(n+1)^11*F(n)^3*n^14+7714278579866682515328*F(n+1)^10*F(n)^4*n^14+1272222795529045848852*F(n+1)^9*F(n)^5*n^14+18229322205371673396*F(n+1)^8*F(n)^6*n^14-4601856038563498572*F(n+1)^7*F(n)^7*n^14-546427387068962256*F(n+1)^6*F(n)^8*n^14-63445805852694408*F(n+1)^5*F(n)^9*n^14-4021418005172568*F(n+1)^4*F(n)^10*n^14+285995928618036*F(n+1)^3*F(n)^11*n^14+10451227298148*F(n+1)^2*F(n)^12*n^14+1425879586404*F(n+1)*F(n)^13*n^14+1400187022813396208865404*F(n+1)^13*F(n)*n^13+1467471247513977297219264*F(n+1)^12*F(n)^2*n^13+462906924925128571579608*F(n+1)^11*F(n)^3*n^13+80556728774512383459612*F(n+1)^10*F(n)^4*n^13-938265406945581520260*F(n+1)^9*F(n)^5*n^13-725980143243072181464*F(n+1)^8*F(n)^6*n^13-57799468985928133464*F(n+1)^7*F(n)^7*n^13-4749801027396493068*F(n+1)^6*F(n)^8*n^13-226252893174880572*F(n+1)^5*F(n)^9*n^13+1012130766246600*F(n+1)^4*F(n)^10*n^13+1929636982911456*F(n+1)^3*F(n)^11*n^13+73733121323316*F(n+1)^2*F(n)^12*n^13+8795535617232*F(n+1)*F(n)^13*n^13+41359849721101168517431080*F(n+1)^13*F(n)*n^12+16500153785775447350325672*F(n+1)^12*F(n)^2*n^12+3182343165946320651468648*F(n+1)^11*F(n)^3*n^12-276097263232555477585782*F(n+1)^10*F(n)^4*n^12-79022723463009674531820*F(n+1)^9*F(n)^5*n^12-4908633173877555862740*F(n+1)^8*F(n)^6*n^12-283788871478118138132*F(n+1)^7*F(n)^7*n^12-9426764208364581078*F(n+1)^6*F(n)^8*n^12+604311950186256312*F(n+1)^5*F(n)^9*n^12+79090630284966300*F(n+1)^4*F(n)^10*n^12+7582072626519300*F(n+1)^3*F(n)^11*n^12+308292924787848*F(n+1)^2*F(n)^12*n^12+32116240208052*F(n+1)*F(n)^13*n^12+251693776103572474280721060*F(n+1)^13*F(n)*n^11+48304705099511357367130260*F(n+1)^12*F(n)^2*n^11-26412283510763415662513844*F(n+1)^11*F(n)^3*n^11-6237414872083539755753688*F(n+1)^10*F(n)^4*n^11-312592668634325449941480*F(n+1)^9*F(n)^5*n^11-8415583153221666862440*F(n+1)^8*F(n)^6*n^11+108782466376277814120*F(n+1)^7*F(n)^7*n^11+79510332838351218804*F(n+1)^6*F(n)^8*n^11+6809937057720024228*F(n+1)^5*F(n)^9*n^11+333664786470555540*F(n+1)^4*F(n)^10*n^11+18673445576265480*F(n+1)^3*F(n)^11*n^11+50050000000000*F(n+1)^13*F(n)*n^21-2259757500000000*F(n+1)^13*F(n)*n^20-3310807500000000*F(n+1)^12*F(n)^2*n^20-185930166296875000*F(n+1)^13*F(n)*n^19-9388504125000000*F(n+1)^12*F(n)^2*n^19+38736447750000000*F(n+1)^11*F(n)^3*n^19+1277025750000000*F(n+1)^10*F(n)^4*n^19+510810300000000*F(n+1)^9*F(n)^5*n^19+259680721456406250*F(n+1)^13*F(n)*n^18+3680961754000781250*F(n+1)^12*F(n)^2*n^18+599797711012500000*F(n+1)^11*F(n)^3*n^18-53603155856250000*F(n+1)^10*F(n)^4*n^18-2017700685000000*F(n+1)^9*F(n)^5*n^18-3907698795000000*F(n+1)^8*F(n)^6*n^18+133784796742097475000*F(n+1)^13*F(n)*n^17+42266845941557737500*F(n+1)^12*F(n)^2*n^17-10959389933842350000*F(n+1)^11*F(n)^3*n^17-2047449601872675000*F(n+1)^10*F(n)^4*n^17-445444751852100000*F(n+1)^9*F(n)^5*n^17-46278646964550000*F(n+1)^8*F(n)^6*n^17+7087055075100000*F(n+1)^7*F(n)^7*n^17+159591732300000*F(n+1)^6*F(n)^8*n^17+35464829400000*F(n+1)^5*F(n)^9*n^17+1008145477131150442500*F(n+1)^13*F(n)*n^16-907332575031807648750*F(n+1)^12*F(n)^2*n^16-262259173710969435000*F(n+1)^11*F(n)^3*n^16-33718723853337022500*F(n+1)^10*F(n)^4*n^16-3761961700048051500*F(n+1)^9*F(n)^5*n^16+810280292556735000*F(n+1)^8*F(n)^6*n^16+117402475705515000*F(n+1)^7*F(n)^7*n^16+1488857869248750*F(n+1)^6*F(n)^8*n^16+299677808430000*F(n+1)^5*F(n)^9*n^16-60644858274000*F(n+1)^4*F(n)^10*n^16-30168916254354662128520*F(n+1)^13*F(n)*n^15-15991208518969159075440*F(n+1)^12*F(n)^2*n^15-1350811609844391079560*F(n+1)^11*F(n)^3*n^15-72954954269538868800*F(n+1)^10*F(n)^4*n^15+89693210260125501120*F(n+1)^9*F(n)^5*n^15+7546440525881178405761550000*F(n+1)^10*F(n)^4+125493147796674902957212500*F(n+1)^9*F(n)^5+1596083659358192529525000*F(n+1)^8*F(n)^6+16249857929497509817500*F(n+1)^7*F(n)^7+128085593045475780000*F(n+1)^6*F(n)^8+530746723298691900*F(n+1)^5*F(n)^9-7575181165351800*F(n+1)^4*F(n)^10-311682653181900*F(n+1)^3*F(n)^11-8461263479760*F(n+1)^2*F(n)^12-235035096660*F(n+1)*F(n)^13-12269457825622427125856160*F(n+1)^8*F(n)^6*n^6-424853985003000482589660*F(n+1)^7*F(n)^7*n^6-11358382240722741640416*F(n+1)^6*F(n)^8*n^6-271755262625231457072*F(n+1)^5*F(n)^9*n^6-6598589435114236560*F(n+1)^4*F(n)^10*n^6-193026934338818580*F(n+1)^3*F(n)^11*n^6-5515203003169860*F(n+1)^2*F(n)^12*n^6-241245246213972*F(n+1)*F(n)^13*n^6-7959918923347172846804542237500*F(n+1)^13*F(n)*n^5-4237724425678368533744269297500*F(n+1)^12*F(n)^2*n^5-270455655371466643865925547500*F(n+1)^11*F(n)^3*n^5-14480281506909654447962523300*F(n+1)^10*F(n)^4*n^5-660207453198902205378490800*F(n+1)^9*F(n)^5*n^5-21121771667705667682623900*F(n+1)^8*F(n)^6*n^5-516783724467960566176560*F(n+1)^7*F(n)^7*n^5-11260102649139052368660*F(n+1)^6*F(n)^8*n^5-253372186827073422108*F(n+1)^5*F(n)^9*n^5-6296279285186850960*F(n+1)^4*F(n)^10*n^5-186410165362621200*F(n+1)^3*F(n)^11*n^5-5516352063642420*F(n+1)^2*F(n)^12*n^5-224066792149200*F(n+1)*F(n)^13*n^5-106267560398802390697004864475000*F(n+1)^13*F(n)*n^4-8174557208843462536702861050000*F(n+1)^12*F(n)^2*n^4-384883125732781013142307912500*F(n+1)^11*F(n)^3*n^4-18335136806530200981902418750*F(n+1)^10*F(n)^4*n^4-565970671784534140404516600*F(n+1)^9*F(n)^5*n^4-12113280963586432969138800*F(n+1)^8*F(n)^6*n^4-231529427147291828454900*F(n+1)^7*F(n)^7*n^4-5206500699335822536650*F(n+1)^6*F(n)^8*n^4-143156674043907123600*F(n+1)^5*F(n)^9*n^4-4129558505655851268*F(n+1)^4*F(n)^10*n^4-126187881041408004*F(n+1)^3*F(n)^11*n^4-3746637022833432*F(n+1)^2*F(n)^12*n^4-140483088774756*F(n+1)*F(n)^13*n^4-39934235827966950071645651662500*F(n+1)^13*F(n)*n^3+3800817325854570373274749837500*F(n+1)^12*F(n)^2*n^3+117984041489945296612019925000*F(n+1)^11*F(n)^3*n^3+5328842024964978268349737500*F(n+1)^10*F(n)^4*n^3+268510246089019526368822500*F(n+1)^9*F(n)^5*n^3+7624274200528129463018700*F(n+1)^8*F(n)^6*n^3+120266400841346719159200*F(n+1)^7*F(n)^7*n^3+399620070755062056900*F(n+1)^6*F(n)^8*n^3-43075366677317274300*F(n+1)^5*F(n)^9*n^3-1857077606549185020*F(n+1)^4*F(n)^10*n^3-59619282339557304*F(n+1)^3*F(n)^11*n^3-1748702903167584*F(n+1)^2*F(n)^12*n^3-60565932908208*F(n+1)*F(n)^13*n^3+348981768727798745034055395562500*F(n+1)^13*F(n)*n^2+21868915788224819242059624637500*F(n+1)^12*F(n)^2*n^2+940653964618774812991915987500*F(n+1)^11*F(n)^3*n^2+32843513430652509662149800000*F(n+1)^10*F(n)^4*n^2+825933213298692420640582500*F(n+1)^9*F(n)^5*n^2+15042077562050082546502500*F(n+1)^8*F(n)^6*n^2+200672765733935489237100*F(n+1)^7*F(n)^7*n^2+1734891496359940175400*F(n+1)^6*F(n)^8*n^2-2169144887965298100*F(n+1)^5*F(n)^9*n^2-549031594925153340*F(n+1)^4*F(n)^10*n^2-18828989481900780*F(n+1)^3*F(n)^11*n^2-20145865428*F(n)^14+825756639598800*F(n+1)^2*F(n)^12*n^11+75775315163184*F(n+1)*F(n)^13*n^11-455220819616362343056577350*F(n+1)^13*F(n)*n^10-1332077179214219212540498590*F(n+1)^12*F(n)^2*n^10-339193799499348241635227040*F(n+1)^11*F(n)^3*n^10-12023348473931028493230972*F(n+1)^10*F(n)^4*n^10+625862285801284666614480*F(n+1)^9*F(n)^5*n^10+73803711038426030221560*F(n+1)^8*F(n)^6*n^10+7804377321775786812060*F(n+1)^7*F(n)^7*n^10+495924676277174824680*F(n+1)^6*F(n)^8*n^10+20000215492115750892*F(n+1)^5*F(n)^9*n^10+630490470762412260*F(n+1)^4*F(n)^10*n^10+27154756679270220*F(n+1)^3*F(n)^11*n^10+1400991981168780*F(n+1)^2*F(n)^12*n^10+115767842610420*F(n+1)*F(n)^13*n^10-29097938125082653969103003900*F(n+1)^13*F(n)*n^9-11026182205466120121158644200*F(n+1)^12*F(n)^2*n^9-2374110751091025539864700*F(n+1)^11*F(n)^3*n^9+119165191608766244979737700*F(n+1)^10*F(n)^4*n^9+8448706968447925860332652*F(n+1)^9*F(n)^5*n^9+577307811431823748652376*F(n+1)^8*F(n)^6*n^9+30175728140462435161488*F(n+1)^7*F(n)^7*n^9+919036522396576805364*F(n+1)^6*F(n)^8*n^9+17748583063843480992*F(n+1)^5*F(n)^9*n^9+260219854156426164*F(n+1)^4*F(n)^10*n^9+11155117369628232*F(n+1)^3*F(n)^11*n^9+1223577044205516*F(n+1)^2*F(n)^12*n^9+98589388545648*F(n+1)*F(n)^13*n^9-153646120052708949964724325900*F(n+1)^13*F(n)*n^8+26045699133390893338316927850*F(n+1)^12*F(n)^2*n^8+9407280663207158558899129200*F(n+1)^11*F(n)^3*n^8+575691827770007634313227600*F(n+1)^10*F(n)^4*n^8+28736123872254055797119580*F(n+1)^9*F(n)^5*n^8+1253727591645178691597556*F(n+1)^8*F(n)^6*n^8+20293757191022533254036*F(n+1)^7*F(n)^7*n^8-609928107400104130638*F(n+1)^6*F(n)^8*n^8-45434176027265997972*F(n+1)^5*F(n)^9*n^8-1591181023405493520*F(n+1)^4*F(n)^10*n^8-47758266363956148*F(n+1)^3*F(n)^11*n^8-508803977249568*F(n+1)^2*F(n)^12*n^8-6722003764476*F(n+1)*F(n)^13*n^8+958083365108982519179186082500*F(n+1)^13*F(n)*n^7+406443680707766343002266920300*F(n+1)^12*F(n)^2*n^7+22597013591148118158360452700*F(n+1)^11*F(n)^3*n^7+503650861122781160424335700*F(n+1)^10*F(n)^4*n^7+7993834777518299903253060*F(n+1)^9*F(n)^5*n^7-1690302189598487036551980*F(n+1)^8*F(n)^6*n^7-140087111423147407253592*F(n+1)^7*F(n)^7*n^7-5761759085021933630208*F(n+1)^6*F(n)^8*n^7-171805647128734764288*F(n+1)^5*F(n)^9*n^7-4514860767494717640*F(n+1)^4*F(n)^10*n^7-133254244881838080*F(n+1)^3*F(n)^11*n^7-3358588855245624*F(n+1)^2*F(n)^12*n^7-152365418661456*F(n+1)*F(n)^13*n^7+7550244467949203649129017790000*F(n+1)^13*F(n)*n^6+286684638858418314212856202500*F(n+1)^12*F(n)^2*n^6-50485067588914805574263636100*F(n+1)^11*F(n)^3*n^6-3511996330504444744634372700*F(n+1)^10*F(n)^4*n^6-239970700758001674857596200*F(n+1)^9*F(n)^5*n^6-540784419401772*F(n+1)^2*F(n)^12*n^2-17345590133508*F(n+1)*F(n)^13*n^2+263402827026463206788535968625000*F(n+1)^13*F(n)*n+19994703216148725353126058937500*F(n+1)^12*F(n)^2*n+951222680001866032416461475000*F(n+1)^11*F(n)^3*n+27641001244395703896448762500*F(n+1)^10*F(n)^4*n+550337327495921373141825000*F(n+1)^9*F(n)^5*n+8197683322441519123717500*F(n+1)^8*F(n)^6*n+94726414377280297755000*F(n+1)^7*F(n)^7*n+802580120563456392300*F(n+1)^6*F(n)^8*n+2481810740212260600*F(n+1)^5*F(n)^9*n-96241634571782700*F(n+1)^4*F(n)^10*n-3584273617393560*F(n+1)^3*F(n)^11*n-100255526230860*F(n+1)^2*F(n)^12*n-2987557228656*F(n+1)*F(n)^13*n+25025000000000*n^21*F(n+1)^14+9058737187500000*n^20*F(n+1)^14+101378528814062500*n^19*F(n+1)^14-6186644859238593750*n^18*F(n+1)^14-64814516099776706250*n^17*F(n+1)^14+1148354493106870645875*n^16*F(n+1)^14+7180281793108785024680*n^15*F(n+1)^14+63504595470075448799868*n^14*F(n+1)^14-20145865428*F(n)^14*n^14+2453144886887755000265920*n^13*F(n+1)^14-282042115992*F(n)^14*n^13-33207043672701792460167510*n^12*F(n+1)^14-1833273753948*F(n)^14*n^12-582937623173428561358548800*n^11*F(n+1)^14-7333095015792*F(n)^14*n^11+2793217480989284891988281550*n^10*F(n+1)^14-20166011293428*F(n)^14*n^10+41554819995369582875112017450*n^9*F(n+1)^14-40332022586856*F(n)^14*n^9-79911355813634142104785066875*n^8*F(n+1)^14-60498033880284*F(n)^14*n^8-1008339937102656035850030402500*n^7*F(n+1)^14-69140610148896*F(n)^14*n^7+432442017867763815401186287500*n^6*F(n+1)^14-60498033880284*F(n)^14*n^6+988445503182636884996534137500*n^5*F(n+1)^14-40332022586856*F(n)^14*n^5+7161647355368291251646222831250*n^4*F(n+1)^14-20166011293428*F(n)^14*n^4+152251226408748516225445675687500*n^3*F(n+1)^14-7333095015792*F(n)^14*n^3-35506788650843118974596609875000*n^2*F(n+1)^14-1833273753948*F(n)^14*n^2-598745991825551898895551893437500*n*F(n+1)^14-282042115992*F(n)^14*n-33672481672556805677564644687500*F(n)*F(n+1)^13+5947490031806060600837884875000*F(n+1)^12*F(n)^2+306962699908482943295043937500*F(n+1)^11*F(n)^3)/F(n+1)^14 which is asymptotic to (1/12069940567016601562500)*(25025000000000*n^21*r^14+50050000000000*n^21*r^13+9058737187500000*n^20*r^14-2259757500000000*n^20*r^13+101378528814062500*n^19*r^14-3310807500000000*n^20*r^12-185930166296875000*n^19*r^13-6186644859238593750*n^18*r^14-9388504125000000*n^19*r^12+259680721456406250*n^18*r^13-64814516099776706250*n^17*r^14+38736447750000000*n^19*r^11+3680961754000781250*n^18*r^12+133784796742097475000*n^17*r^13+1148354493106870645875*n^16*r^14+1277025750000000*n^19*r^10+599797711012500000*n^18*r^11+42266845941557737500*n^17*r^12+1008145477131150442500*n^16*r^13+7180281793108785024680*n^15*r^14+510810300000000*n^19*r^9-53603155856250000*n^18*r^10-10959389933842350000*n^17*r^11-907332575031807648750*n^16*r^12-30168916254354662128520*n^15*r^13+63504595470075448799868*n^14*r^14-2017700685000000*n^18*r^9-2047449601872675000*n^17*r^10-262259173710969435000*n^16*r^11-15991208518969159075440*n^15*r^12-378313758212133261705036*n^14*r^13+2453144886887755000265920*n^13*r^14-3907698795000000*n^18*r^8-445444751852100000*n^17*r^9-33718723853337022500*n^16*r^10-1350811609844391079560*n^15*r^11-195519766554738787248*n^14*r^12+1400187022813396208865404*n^13*r^13-33207043672701792460167510*n^12*r^14-46278646964550000*n^17*r^8-3761961700048051500*n^16*r^9-72954954269538868800*n^15*r^10+14711647292469455264496*n^14*r^11+1467471247513977297219264*n^13*r^12+41359849721101168517431080*n^12*r^13-582937623173428561358548800*n^11*r^14+7087055075100000*n^17*r^7+810280292556735000*n^16*r^8+89693210260125501120*n^15*r^9+7714278579866682515328*n^14*r^10+462906924925128571579608*n^13*r^11+16500153785775447350325672*n^12*r^12+251693776103572474280721060*n^11*r^13+2793217480989284891988281550*n^10*r^14+159591732300000*n^17*r^6+117402475705515000*n^16*r^7+14269881735367778520*n^15*r^8+1272222795529045848852*n^14*r^9+80556728774512383459612*n^13*r^10+3182343165946320651468648*n^12*r^11+48304705099511357367130260*n^11*r^12-455220819616362343056577350*n^10*r^13+41554819995369582875112017450*n^9*r^14+35464829400000*n^17*r^5+1488857869248750*n^16*r^6+375148471128528240*n^15*r^7+18229322205371673396*n^14*r^8-938265406945581520260*n^13*r^9-276097263232555477585782*n^12*r^10-26412283510763415662513844*n^11*r^11-1332077179214219212540498590*n^10*r^12-29097938125082653969103003900*n^9*r^13-79911355813634142104785066875*n^8*r^14+299677808430000*n^16*r^5-16655470438103640*n^15*r^6-4601856038563498572*n^14*r^7-725980143243072181464*n^13*r^8-79022723463009674531820*n^12*r^9-6237414872083539755753688*n^11*r^10-339193799499348241635227040*n^10*r^11-11026182205466120121158644200*n^9*r^12-153646120052708949964724325900*n^8*r^13-1008339937102656035850030402500*n^7*r^14-60644858274000*n^16*r^4-4042347118266600*n^15*r^5-546427387068962256*n^14*r^6-57799468985928133464*n^13*r^7-4908633173877555862740*n^12*r^8-312592668634325449941480*n^11*r^9-12023348473931028493230972*n^10*r^10-2374110751091025539864700*n^9*r^11+26045699133390893338316927850*n^8*r^12+958083365108982519179186082500*n^7*r^13+432442017867763815401186287500*n^6*r^14-874179672846480*n^15*r^4-63445805852694408*n^14*r^5-4749801027396493068*n^13*r^6-283788871478118138132*n^12*r^7-8415583153221666862440*n^11*r^8+625862285801284666614480*n^10*r^9+119165191608766244979737700*n^9*r^10+9407280663207158558899129200*n^8*r^11+406443680707766343002266920300*n^7*r^12+7550244467949203649129017790000*n^6*r^13+988445503182636884996534137500*n^5*r^14+18837627747120*n^15*r^3-4021418005172568*n^14*r^4-226252893174880572*n^13*r^5-9426764208364581078*n^12*r^6+108782466376277814120*n^11*r^7+73803711038426030221560*n^10*r^8+8448706968447925860332652*n^9*r^9+575691827770007634313227600*n^8*r^10+22597013591148118158360452700*n^7*r^11+286684638858418314212856202500*n^6*r^12-7959918923347172846804542237500*n^5*r^13+7161647355368291251646222831250*n^4*r^14+678990279240*n^15*r^2+285995928618036*n^14*r^3+1012130766246600*n^13*r^4+604311950186256312*n^12*r^5+79510332838351218804*n^11*r^6+7804377321775786812060*n^10*r^7+577307811431823748652376*n^9*r^8+28736123872254055797119580*n^8*r^9+503650861122781160424335700*n^7*r^10-50485067588914805574263636100*n^6*r^11-4237724425678368533744269297500*n^5*r^12-106267560398802390697004864475000*n^4*r^13+152251226408748516225445675687500*n^3*r^14+104460042960*n^15*r+10451227298148*n^14*r^2+1929636982911456*n^13*r^3+79090630284966300*n^12*r^4+6809937057720024228*n^11*r^5+495924676277174824680*n^10*r^6+30175728140462435161488*n^9*r^7+1253727591645178691597556*n^8*r^8+7993834777518299903253060*n^7*r^9-3511996330504444744634372700*n^6*r^10-270455655371466643865925547500*n^5*r^11-8174557208843462536702861050000*n^4*r^12-39934235827966950071645651662500*n^3*r^13-35506788650843118974596609875000*n^2*r^14+1425879586404*n^14*r+73733121323316*n^13*r^2+7582072626519300*n^12*r^3+333664786470555540*n^11*r^4+20000215492115750892*n^10*r^5+919036522396576805364*n^9*r^6+20293757191022533254036*n^8*r^7-1690302189598487036551980*n^7*r^8-239970700758001674857596200*n^6*r^9-14480281506909654447962523300*n^5*r^10-384883125732781013142307912500*n^4*r^11+3800817325854570373274749837500*n^3*r^12+348981768727798745034055395562500*n^2*r^13-598745991825551898895551893437500*n*r^14-20145865428*n^14+8795535617232*n^13*r+308292924787848*n^12*r^2+18673445576265480*n^11*r^3+630490470762412260*n^10*r^4+17748583063843480992*n^9*r^5-609928107400104130638*n^8*r^6-140087111423147407253592*n^7*r^7-12269457825622427125856160*n^6*r^8-660207453198902205378490800*n^5*r^9-18335136806530200981902418750*n^4*r^10+117984041489945296612019925000*n^3*r^11+21868915788224819242059624637500*n^2*r^12+263402827026463206788535968625000*n*r^13-282042115992*n^13+32116240208052*n^12*r+825756639598800*n^11*r^2+27154756679270220*n^10*r^3+260219854156426164*n^9*r^4-45434176027265997972*n^8*r^5-5761759085021933630208*n^7*r^6-424853985003000482589660*n^6*r^7-21121771667705667682623900*n^5*r^8-565970671784534140404516600*n^4*r^9+5328842024964978268349737500*n^3*r^10+940653964618774812991915987500*n^2*r^11+19994703216148725353126058937500*n*r^12-33672481672556805677564644687500*r^13-1833273753948*n^12+75775315163184*n^11*r+1400991981168780*n^10*r^2+11155117369628232*n^9*r^3-1591181023405493520*n^8*r^4-171805647128734764288*n^7*r^5-11358382240722741640416*n^6*r^6-516783724467960566176560*n^5*r^7-12113280963586432969138800*n^4*r^8+268510246089019526368822500*n^3*r^9+32843513430652509662149800000*n^2*r^10+951222680001866032416461475000*n*r^11+5947490031806060600837884875000*r^12-7333095015792*n^11+115767842610420*n^10*r+1223577044205516*n^9*r^2-47758266363956148*n^8*r^3-4514860767494717640*n^7*r^4-271755262625231457072*n^6*r^5-11260102649139052368660*n^5*r^6-231529427147291828454900*n^4*r^7+7624274200528129463018700*n^3*r^8+825933213298692420640582500*n^2*r^9+27641001244395703896448762500*n*r^10+306962699908482943295043937500*r^11-20166011293428*n^10+98589388545648*n^9*r-508803977249568*n^8*r^2-133254244881838080*n^7*r^3-6598589435114236560*n^6*r^4-253372186827073422108*n^5*r^5-5206500699335822536650*n^4*r^6+120266400841346719159200*n^3*r^7+15042077562050082546502500*n^2*r^8+550337327495921373141825000*n*r^9+7546440525881178405761550000*r^10-40332022586856*n^9-6722003764476*n^8*r-3358588855245624*n^7*r^2-193026934338818580*n^6*r^3-6296279285186850960*n^5*r^4-143156674043907123600*n^4*r^5+399620070755062056900*n^3*r^6+200672765733935489237100*n^2*r^7+8197683322441519123717500*n*r^8+125493147796674902957212500*r^9-60498033880284*n^8-152365418661456*n^7*r-5515203003169860*n^6*r^2-186410165362621200*n^5*r^3-4129558505655851268*n^4*r^4-43075366677317274300*n^3*r^5+1734891496359940175400*n^2*r^6+94726414377280297755000*n*r^7+1596083659358192529525000*r^8-69140610148896*n^7-241245246213972*n^6*r-5516352063642420*n^5*r^2-126187881041408004*n^4*r^3-1857077606549185020*n^3*r^4-2169144887965298100*n^2*r^5+802580120563456392300*n*r^6+16249857929497509817500*r^7-60498033880284*n^6-224066792149200*n^5*r-3746637022833432*n^4*r^2-59619282339557304*n^3*r^3-549031594925153340*n^2*r^4+2481810740212260600*n*r^5+128085593045475780000*r^6-40332022586856*n^5-140483088774756*n^4*r-1748702903167584*n^3*r^2-18828989481900780*n^2*r^3-96241634571782700*n*r^4+530746723298691900*r^5-20166011293428*n^4-60565932908208*n^3*r-540784419401772*n^2*r^2-3584273617393560*n*r^3-7575181165351800*r^4-7333095015792*n^3-17345590133508*n^2*r-100255526230860*n*r^2-311682653181900*r^3-1833273753948*n^2-2987557228656*n*r-8461263479760*r^2-282042115992*n-235035096660*r-20145865428)/r^14 The limit of the standardized moment is, 135135 Theorem, 15 Central moment, 15, of X_n is 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1-29877354514817769960*F(n+1)^5*F(n)^10*n^11-967255805408092200*F(n+1)^4*F(n)^11*n^11-41950050618949200*F(n+1)^3*F(n)^12*n^11-1831445703196200*F(n+1)^2*F(n)^13*n^11-147340890595080*F(n+1)*F(n)^14*n^11+610244430475752351887533125200*F(n+1)^14*F(n)*n^10+299212465647369019641670775000*F(n+1)^13*F(n)^2*n^10+62038017384693044622633763200*F(n+1)^12*F(n)^3*n^10+1149367580141086303639012800*F(n+1)^11*F(n)^4*n^10-272400637016178246652444368*F(n+1)^10*F(n)^5*n^10-18351624709196947327018860*F(n+1)^9*F(n)^6*n^10-1088973419203079116003440*F(n+1)^8*F(n)^7*n^10-54350643819502459837980*F(n+1)^7*F(n)^8*n^10-1772951913285092448480*F(n+1)^6*F(n)^9*n^10-42091920930182661252*F(n+1)^5*F(n)^10*n^10-893452991826114720*F(n+1)^4*F(n)^11*n^10-35107085026393380*F(n+1)^3*F(n)^12*n^10-2141274190615560*F(n+1)^2*F(n)^13*n^10-164890177812360*F(n+1)*F(n)^14*n^10+5771553558654539818798749685000*F(n+1)^14*F(n)*n^9+1708717646002889401342088912000*F(n+1)^13*F(n)^2*n^9-2251201296093750000*F(n+1)^11*F(n)^4*n^19+150369782062500000*F(n+1)^10*F(n)^5*n^19+2554051500000000*F(n+1)^9*F(n)^6*n^19+6567561000000000*F(n+1)^8*F(n)^7*n^19-389617728350735625000*F(n+1)^14*F(n)*n^18-1272675535440318750000*F(n+1)^13*F(n)^2*n^18-245434266074497500000*F(n+1)^12*F(n)^3*n^18+37300948644960000000*F(n+1)^11*F(n)^4*n^18+5490007857959625000*F(n+1)^10*F(n)^5*n^18+879915893731875000*F(n+1)^9*F(n)^6*n^18+84885725925000000*F(n+1)^8*F(n)^7*n^18-10270023513750000*F(n+1)^7*F(n)^8*n^18-197026830000000*F(n+1)^6*F(n)^9*n^18-39405366000000*F(n+1)^5*F(n)^10*n^18-40825428818599339035000*F(n+1)^14*F(n)*n^17-12140705610819119100000*F(n+1)^13*F(n)^2*n^17+4666144007872833525000*F(n+1)^12*F(n)^3*n^17+960161763980519100000*F(n+1)^11*F(n)^4*n^17+87298831359594855000*F(n+1)^10*F(n)^5*n^17+8328834086157585000*F(n+1)^9*F(n)^6*n^17-1277524452010950000*F(n+1)^8*F(n)^7*n^17-180112569211575000*F(n+1)^7*F(n)^8*n^17-1932833202300000*F(n+1)^6*F(n)^9*n^17-374153950170000*F(n+1)^5*F(n)^10*n^17+60935025060000*F(n+1)^4*F(n)^11*n^17-244114863924472116808150*F(n+1)^14*F(n)*n^16+327210023117677930556300*F(n+1)^13*F(n)^2*n^16+91499469471803328854400*F(n+1)^12*F(n)^3*n^16+5039115410950557356700*F(n+1)^11*F(n)^4*n^16+233061495249766528800*F(n+1)^10*F(n)^5*n^16-172678898883689616600*F(n+1)^9*F(n)^6*n^16-25340410990311931800*F(n+1)^8*F(n)^7*n^16-705303437777517150*F(n+1)^7*F(n)^8*n^16+20469504948621300*F(n+1)^6*F(n)^9*n^16+4130929818100800*F(n+1)^5*F(n)^10*n^16+939531036389400*F(n+1)^4*F(n)^11*n^16-17279432106300*F(n+1)^3*F(n)^12*n^16-562477154400*F(n+1)^2*F(n)^13*n^16-80353879200*F(n+1)*F(n)^14*n^16+10359663001727885102540560*F(n+1)^14*F(n)*n^15+4913754508793001830420840*F(n+1)^13*F(n)^2*n^15+31323645749709541370880*F(n+1)^12*F(n)^3*n^15-51281408646425707472520*F(n+1)^11*F(n)^4*n^15-19184731025584640338368*F(n+1)^10*F(n)^5*n^15-2741533428645194634360*F(n+1)^9*F(n)^6*n^15-54149354467322039640*F(n+1)^8*F(n)^7*n^15+6170047180556379120*F(n+1)^7*F(n)^8*n^15+710743914105259320*F(n+1)^6*F(n)^9*n^15+74843989975950624*F(n+1)^5*F(n)^10*n^15+4923880814984040*F(n+1)^4*F(n)^11*n^15-279500254946640*F(n+1)^3*F(n)^12*n^15-9212572250280*F(n+1)^2*F(n)^13*n^15-1177184330280*F(n+1)*F(n)^14*n^15+112108913066560581303121360*F(n+1)^14*F(n)*n^14-17295526614039619064835020*F(n+1)^13*F(n)^2*n^14-8365895107119882324299160*F(n+1)^12*F(n)^3*n^14-1594714736057588753772780*F(n+1)^11*F(n)^4*n^14-221211015813088131743640*F(n+1)^10*F(n)^5*n^14-638002666512955385460*F(n+1)^9*F(n)^6*n^14+1196402045451937758720*F(n+1)^8*F(n)^7*n^14+89813312299897732260*F(n+1)^7*F(n)^8*n^14+6629912625668698080*F(n+1)^6*F(n)^9*n^14+321349693702262940*F(n+1)^5*F(n)^10*n^14)/F(n+1)^15 which is asymptotic to -(1/67055225372314453125000)*(2690187500000000*n^22*r^15-500500000000000*n^22*r^14+64198509375000000*n^21*r^15-500500000000000*n^22*r^13+7688931250000000*n^21*r^14-3662323185614843750*n^20*r^15+15002487500000000*n^21*r^13+1293579518481250000*n^20*r^14-67014487719867187500*n^19*r^15+17342325000000000*n^21*r^12+1314083927406250000*n^20*r^13+45952269261335937500*n^19*r^14+2323554929892803343750*n^18*r^15+97006659750000000*n^20*r^12-3574829234539062500*n^19*r^13-389617728350735625000*n^18*r^14+33651984606865603470000*n^17*r^15-136145134125000000*n^20*r^11-18685093223671875000*n^19*r^12-1272675535440318750000*n^18*r^13-40825428818599339035000*n^17*r^14-501530102840997655781425*n^16*r^15-3064861800000000*n^20*r^10-2251201296093750000*n^19*r^11-245434266074497500000*n^18*r^12-12140705610819119100000*n^17*r^13-244114863924472116808150*n^16*r^14-5750352606777357636413808*n^15*r^15-1021620600000000*n^20*r^9+150369782062500000*n^19*r^10+37300948644960000000*n^18*r^11+4666144007872833525000*n^17*r^12+327210023117677930556300*n^16*r^13+10359663001727885102540560*n^15*r^14+19067569264283024106341800*n^14*r^15+2554051500000000*n^19*r^9+5490007857959625000*n^18*r^10+960161763980519100000*n^17*r^11+91499469471803328854400*n^16*r^12+4913754508793001830420840*n^15*r^13+112108913066560581303121360*n^14*r^14-114567870884272704709851600*n^13*r^15+6567561000000000*n^19*r^8+879915893731875000*n^18*r^9+87298831359594855000*n^17*r^10+5039115410950557356700*n^16*r^11+31323645749709541370880*n^15*r^12-17295526614039619064835020*n^14*r^13-858939148797704902097363200*n^13*r^14+5396581719791279691047809500*n^12*r^15+84885725925000000*n^18*r^8+8328834086157585000*n^17*r^9+233061495249766528800*n^16*r^10-51281408646425707472520*n^15*r^11-8365895107119882324299160*n^14*r^12-571166401807673768734281560*n^13*r^13-14918976492774735307493732100*n^12*r^14+118369135119796428697807610100*n^11*r^15-10270023513750000*n^18*r^7-1277524452010950000*n^17*r^8-172678898883689616600*n^16*r^9-19184731025584640338368*n^15*r^10-1594714736057588753772780*n^14*r^11-88837214557522966461871560*n^13*r^12-2610559861939356349592380200*n^12*r^13-18218399322968279503998177300*n^11*r^14-625332064138726322761044697750*n^10*r^15-197026830000000*n^18*r^6-180112569211575000*n^17*r^7-25340410990311931800*n^16*r^8-2741533428645194634360*n^15*r^9-221211015813088131743640*n^14*r^10-11982075400777805104435920*n^13*r^11-278113316314893178539976920*n^12*r^12+10420987971873529279631052300*n^11*r^13+610244430475752351887533125200*n^10*r^14-10770201677068540124373094425000*n^9*r^15-39405366000000*n^18*r^5-1932833202300000*n^17*r^6-705303437777517150*n^16*r^7-54149354467322039640*n^15*r^8-638002666512955385460*n^14*r^9+496002312130890196915920*n^13*r^10+78464601054882173561672970*n^12*r^11+6515677756123731605204098200*n^11*r^12+299212465647369019641670775000*n^10*r^13+5771553558654539818798749685000*n^9*r^14+22892479733661933514939100490625*n^8*r^15-374153950170000*n^17*r^5+20469504948621300*n^16*r^6+6170047180556379120*n^15*r^7+1196402045451937758720*n^14*r^8+161811938924898607963800*n^13*r^9+16463536545158910062675820*n^12*r^10+1231198964676725873114711880*n^11*r^11+62038017384693044622633763200*n^10*r^12+1708717646002889401342088912000*n^9*r^13+14798294469502628507198579293750*n^8*r^14+346300168625032506303017244750000*n^7*r^15+60935025060000*n^17*r^4+4130929818100800*n^16*r^5+710743914105259320*n^15*r^6+89813312299897732260*n^14*r^7+9462746765155001277960*n^13*r^8+789534555947486459919900*n^12*r^9+46063113558650838674748360*n^11*r^10+1149367580141086303639012800*n^10*r^11-76721974289093701359813879000*n^9*r^12-8344000305719670436138897362500*n^8*r^13-247171493411558870381346100150000*n^7*r^14-260323898425117798765198204012500*n^6*r^15+939531036389400*n^16*r^4+74843989975950624*n^15*r^5+6629912625668698080*n^14*r^6+487715410095001648560*n^13*r^7+22046102986381302628800*n^12*r^8-658567159023383002411200*n^11*r^9-272400637016178246652444368*n^10*r^10-31855800192228645397785306000*n^9*r^11-2206127164515469424563494303000*n^8*r^12-87772610912814669697518979550000*n^7*r^13-1488120052824289385621257672275000*n^6*r^14-3093607156789587337551317152875000*n^5*r^15-17279432106300*n^16*r^3+4923880814984040*n^15*r^4+321349693702262940*n^14*r^5+17676475532808412320*n^13*r^6+238873218144340549770*n^12*r^7-110657774447191601487000*n^11*r^8-18351624709196947327018860*n^10*r^9-1757096868845558626393807800*n^9*r^10-108231072251571284328157630500*n^8*r^11-3550466118151379609884010205000*n^7*r^12+2226682023911426391174771075000*n^6*r^13+3118361784887454713760607235850000*n^5*r^14-141515660621881575483927793593750*n^4*r^15-562477154400*n^16*r^2-279500254946640*n^15*r^3+3066842401262640*n^14*r^4-424197938265421320*n^13*r^5-87998989786285998420*n^12*r^6-11347784309811061312200*n^11*r^7-1088973419203079116003440*n^10*r^8-74581700333749085072756160*n^9*r^9-2694226784381693595319685400*n^8*r^10+95982035568964332716019663000*n^7*r^11+20229592506503891608993547925000*n^6*r^12+1196686081848525134223218150250000*n^5*r^13+26765016544650469695227989643437500*n^4*r^14-13581048292202426012550592492500000*n^3*r^15-80353879200*n^16*r-9212572250280*n^15*r^2-2030566856752980*n^14*r^3-80263934192496600*n^13*r^4-8263998777548634120*n^12*r^5-721027759808617541280*n^11*r^6-54350643819502459837980*n^10*r^7-3052290426731162193428280*n^9*r^8-72634669633796676012406800*n^8*r^9+7669327832935775970478515000*n^7*r^10+1086815274017326490734284915000*n^6*r^11+63498457188941424211537168050000*n^5*r^12+1556571986206777355340881656125000*n^4*r^13-2253905851402287563824396541250000*n^3*r^14+5549167405588877664926760379687500*n^2*r^15-1177184330280*n^15*r-69622618632840*n^14*r^2-8712965756607840*n^13*r^3-414000626894290800*n^12*r^4-29877354514817769960*n^11*r^5-1772951913285092448480*n^10*r^6-72183620781963028320840*n^9*r^7+743200654423633757825760*n^8*r^8+466785191180984061217431600*n^7*r^9+45259939689491072267445578400*n^6*r^10+2201114741517971630901704700000*n^5*r^11+22006316523549370171137865875000*n^4*r^12-3204834079597268779350633684375000*n^3*r^13-117113988998816290030848243255000000*n^2*r^14+111556091349919091869941231016875000*n*r^15+14463698256*n^15-7862627079720*n^14*r-315626019803640*n^13*r^2-24039694361510100*n^12*r^3-967255805408092200*n^11*r^4-42091920930182661252*n^10*r^5-389973042364041484920*n^9*r^6+171382283384899179788910*n^8*r^7+23312450792538584254492200*n^7*r^8+1804095658609297519327980300*n^6*r^9+82145444687314076425643559000*n^5*r^10+872950578695425431779508843750*n^4*r^11-131406698282134555530037045125000*n^3*r^12-6424172857579479368761338449062500*n^2*r^13-46071743828991903080162926025625000*n*r^14+216955473840*n^14-31470596788680*n^13*r-935491914728280*n^12*r^2-41950050618949200*n^11*r^3-893452991826114720*n^10*r^4+30742631527310857440*n^9*r^5+7974823571641602638820*n^8*r^6+808270483070431448701920*n^7*r^7+55735046785564668186865200*n^6*r^8+2454702919954002035115688800*n^5*r^9+32261436456741501184774462500*n^4*r^10-3572553270328632519171310125000*n^3*r^11-212688696700142003942395245000000*n^2*r^12-2442494751700369607687790585000000*n*r^13+46372991872822985743224765305625000*r^14+1518688316880*n^13-82993504131720*n^12*r-1831445703196200*n^11*r^2-35107085026393380*n^10*r^3+1335814015493837880*n^9*r^4+241864775023246741080*n^8*r^5+21440231054753529241080*n^7*r^6+1347706300943168076210300*n^6*r^7+55496869865677680396957000*n^5*r^8+595311869936104134164032500*n^4*r^9-95797029427169799117507300000*n^3*r^10-6337140624451536374845455187500*n^2*r^11-130805611055086194932645143125000*n*r^12+336724816725568056775646446875000*r^13+6580982706480*n^12-147340890595080*n^11*r-2141274190615560*n^10*r^2+33246915713051040*n^9*r^3+6126141220522923600*n^8*r^4+494047993780992016080*n^7*r^5+28341259895791572649920*n^6*r^6+1072137090999572386588800*n^5*r^7+7573513558894898526054000*n^4*r^8-2189227391169920453508975000*n^3*r^9-151403914738198286347365000000*n^2*r^10-4201495474274411419002150000000*n*r^11-29737450159030303004189424375000*r^12+19742948119440*n^11-164890177812360*n^10*r-529142347613880*n^9*r^2+164938917127404420*n^8*r^3+11147697311626675800*n^7*r^4+585081667579677608340*n^6*r^5+20653953683121976417200*n^5*r^6+161407847342746715460750*n^4*r^7-37725465103940828374875000*n^3*r^8-2752734634056973230117862500*n^2*r^9-88006211006812198621773525000*n*r^10-1023208999694943144316813125000*r^11+43434485862768*n^10-70667219062440*n^9*r+3297229026010920*n^8*r^2+297302161367811600*n^7*r^3+12931581747912937200*n^6*r^4+441974516914119813624*n^5*r^5+6055995710054760970500*n^4*r^6-457271940011382488421000*n^3*r^7-38716112141459430420600000*n^2*r^8-1351690501903816208752800000*n*r^9-18866101314702946014403875000*r^10+72390809771280*n^9+122374940327640*n^8*r+7459126057623240*n^7*r^2+345626378316519300*n^6*r^3+10452614336008430040*n^5*r^4+207721753170163432200*n^4*r^5-2647970211907858266000*n^3*r^6-421657086311938835572500*n^2*r^7-16320561424087273578225000*n*r^8-250986295593349805914425000*r^9+93073898277360*n^8+302777434519560*n^7*r+9235573548201000*n^6*r^2+284635673151953760*n^5*r^3+6000008689956612240*n^4*r^4+50568492086378580600*n^3*r^5-3166859155902248664000*n^2*r^6-158495344571622994650000*n*r^7-2660139432263654215875000*r^8+93073898277360*n^7+357932337202440*n^6*r+7740436953314520*n^5*r^2+169123006114810020*n^4*r^3+2410514060959204200*n^3*r^4-282330579775315500*n^2*r^5-1162786698097447995000*n*r^6-23214082756425014025000*r^7+72390809771280*n^6+280422985326120*n^5*r+4587206096523960*n^4*r^2+71379044615183760*n^3*r^3+646139220663081600*n^2*r^4-3340883569451313600*n*r^5-160106991306844725000*r^6+43434485862768*n^5+154653093602280*n^4*r+1909855018519560*n^3*r^2+20386958792627700*n^2*r^3+103894014610549800*n*r^4-589718581442991000*r^5+19742948119440*n^4+59931940801320*n^3*r+534501951356520*n^2*r^2+3542704323631200*n*r^3+7575181165351800*r^4+6580982706480*n^3+15640882586280*n^2*r+90619087267800*n*r^2+283347866529000*r^3+1518688316880*n^2+2478917173320*n*r+7051052899800*r^2+216955473840*n+180796228200*r+14463698256)/r^15 The limit of the standardized moment is, 0 Theorem, 16 Central moment, 16, of X_n is 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958510246117320*F(n+1)^10*F(n)^6*n^13-29290294334449848640875480*F(n+1)^9*F(n)^7*n^13-824677431688594099095480*F(n+1)^8*F(n)^8*n^13-16471650020235053503860*F(n+1)^7*F(n)^9*n^13+1441739854145495464560*F(n+1)^6*F(n)^10*n^13+159967097575276314960*F(n+1)^5*F(n)^11*n^13+8269286368852929420*F(n+1)^4*F(n)^12*n^13+504183918469533120*F(n+1)^3*F(n)^13*n^13+17520998634107640*F(n+1)^2*F(n)^14*n^13+1501114923498960*F(n+1)*F(n)^15*n^13+87644120887559713663725983559180*F(n+1)^15*F(n)*n^12+4620606094460209072677401473920*F(n+1)^14*F(n)^2*n^12-983391534843379201487555995140*F(n+1)^13*F(n)^3*n^12-386106370444349946848011736610*F(n+1)^12*F(n)^4*n^12-60486545323346835485967141240*F(n+1)^11*F(n)^5*n^12-2310445326895720017612123060*F(n+1)^10*F(n)^6*n^12-3445345860262251687186120*F(n+1)^9*F(n)^7*n^12+2360323191110459892521490*F(n+1)^8*F(n)^8*n^12+255920661272221487401860*F(n+1)^7*F(n)^9*n^12+16538883259116399281100*F(n+1)^6*F(n)^10*n^12+701991345723227469000*F(n+1)^5*F(n)^11*n^12+23114871090249382080*F(n+1)^4*F(n)^12*n^12+1015586548207817040*F(n+1)^3*F(n)^13*n^12+38669384313083160*F(n+1)^2*F(n)^14*n^12+3020671062274320*F(n+1)*F(n)^15*n^12-146938320005529289324298544423480*F(n+1)^15*F(n)*n^11+5317812500000000*n^24*F(n+1)^16+450844143750000000*n^23*F(n+1)^16+3243526614453125000*n^22*F(n+1)^16-377084235812972187500*n^21*F(n+1)^16+16370398776356811875000*n^20*F(n+1)^16+448416942547572100557500*n^19*F(n+1)^16-13328391832715202418181500*n^18*F(n+1)^16-239580123205926135485189490*n^17*F(n+1)^16+3321937734993413610982079954*n^16*F(n+1)^16-177826004451*F(n)^16*n^16+49204272973240383682201706440*n^15*F(n+1)^16-257307429211999840003033079908200000*F(n+1)^13*F(n)^3*n^5-5281076934627514269546656155635000*F(n+1)^12*F(n)^4*n^5-141097921077609626592472053772500*F(n+1)^11*F(n)^5*n^5-4197412284601890567380424369840*F(n+1)^10*F(n)^6*n^5-93390290619983998807855857480*F(n+1)^9*F(n)^7*n^5-1658120366187393121961333100*F(n+1)^8*F(n)^8*n^5-28409440947376083013479060*F(n+1)^7*F(n)^9*n^5-546810268585514835021120*F(n+1)^6*F(n)^10*n^5-11961233531147270929104*F(n+1)^5*F(n)^11*n^5-275167673033957203500*F(n+1)^4*F(n)^12*n^5-6951091533050115360*F(n+1)^3*F(n)^13*n^5-174455740636271640*F(n+1)^2*F(n)^14*n^5-5705712006518160*F(n+1)*F(n)^15*n^5-113726483677900127230031822235402093750*F(n+1)^15*F(n)*n^4-4753752335257582623265949498817712500*F(n+1)^14*F(n)^2*n^4+151916484809039039315503324562475000*F(n+1)^13*F(n)^3*n^4+6784668081081273905805286375987500*F(n+1)^12*F(n)^4*n^4+125577188646254541213893006580000*F(n+1)^11*F(n)^5*n^4+2348215376538213202206102052500*F(n+1)^10*F(n)^6*n^4+48772710155320709796215335800*F(n+1)^9*F(n)^7*n^4+788017336290491179842233550*F(n+1)^8*F(n)^8*n^4+6724513404012243509712900*F(n+1)^7*F(n)^9*n^4-70626367438052799061260*F(n+1)^6*F(n)^10*n^4-4758643914399958850280*F(n+1)^5*F(n)^11*n^4-140626538633210862960*F(n+1)^4*F(n)^12*n^4-3683174726314072080*F(n+1)^3*F(n)^13*n^4-91875978628552440*F(n+1)^2*F(n)^14*n^4-2814129451178640*F(n+1)*F(n)^15*n^4+64942723601288507785687955308100250000*F(n+1)^15*F(n)*n^3+22391018153115704318110413550216500000*F(n+1)^14*F(n)^2*n^3+896632217742281286812695050057975000*F(n+1)^13*F(n)^3*n^3+21255354385249689225359715351825000*F(n+1)^12*F(n)^4*n^3+456910674695700267906460876725000*F(n+1)^11*F(n)^5*n^3+9090897330923785899317381040000*F(n+1)^10*F(n)^6*n^3+151235710229646240563640015000*F(n+1)^9*F(n)^7*n^3+2003603702349225844497930300*F(n+1)^8*F(n)^8*n^3+20143676433485811136530600*F(n+1)^7*F(n)^9*n^3+118212077431603790949600*F(n+1)^6*F(n)^10*n^3-928690148391943724280*F(n+1)^5*F(n)^11*n^3-51091634786859674280*F(n+1)^4*F(n)^12*n^3-1404973969882557480*F(n+1)^3*F(n)^13*n^3-34549089928470360*F(n+1)^2*F(n)^14*n^3-991083598140240*F(n+1)*F(n)^15*n^3+629333505062483350880740590226888031250*F(n+1)^15*F(n)*n^2+31092793420158771524772563644139250000*F(n+1)^14*F(n)^2*n^2+827592943396753998719703211203000000*F(n+1)^13*F(n)^3*n^2+21158488177323714082708814639587500*F(n+1)^12*F(n)^4*n^2+484781741238488740401362877045000*F(n+1)^11*F(n)^5*n^2+8796775961140745813429774580000*F(n+1)^10*F(n)^6*n^2+125600285571730800081369300000*F(n+1)^9*F(n)^7*n^2+1443155510185185655298261250*F(n+1)^8*F(n)^8*n^2+13307645143390486011680700*F(n+1)^7*F(n)^9*n^2+88234594216009355022480*F(n+1)^6*F(n)^10*n^2+65448475892987728320*F(n+1)^5*F(n)^11*n^2-12531855461117412420*F(n+1)^4*F(n)^12*n^2-366281671746168360*F(n+1)^3*F(n)^13*n^2-8832551779598040*F(n+1)^2*F(n)^14*n^2-237628231133040*F(n+1)*F(n)^15*n^2+106271675911686957467184982209881812500*F(n+1)^15*F(n)*n+494339679648469866247962946367625000*F(n+1)^14*F(n)^2*n+197752533754422733629023998656000000*F(n+1)^13*F(n)^3*n+9858731477652484987716733507312500*F(n+1)^12*F(n)^4*n+240021702840940628965343421570000*F(n+1)^11*F(n)^5*n+3925271917551853536406178895000*F(n+1)^10*F(n)^6*n+49042555910806054256370360000*F(n+1)^9*F(n)^7*n+497789780428544870042741250*F(n+1)^8*F(n)^8*n-54842152691259199110801088917720*F(n+1)^11*F(n)^5*n^7-1954033025996622430220370216480*F(n+1)^10*F(n)^6*n^7-69632573134592985184000518120*F(n+1)^9*F(n)^7*n^7-2075844125661796778655612960*F(n+1)^8*F(n)^8*n^7-49546093237378582681877040*F(n+1)^7*F(n)^9*n^7-1017308372905644168131640*F(n+1)^6*F(n)^10*n^7-19855020809215137457080*F(n+1)^5*F(n)^11*n^7-402892048748708850240*F(n+1)^4*F(n)^12*n^7-9854497161308119320*F(n+1)^3*F(n)^13*n^7-237074731228815480*F(n+1)^2*F(n)^14*n^7-8664736720582800*F(n+1)*F(n)^15*n^7+4355233493754829078679685907824922500*F(n+1)^15*F(n)*n^6-308098541995271174118787738119832500*F(n+1)^14*F(n)^2*n^6-111667953242056690000307304635220000*F(n+1)^13*F(n)^3*n^6-5182646784576587454958002579802500*F(n+1)^12*F(n)^4*n^6-151843121867779342080981878643120*F(n+1)^11*F(n)^5*n^6-4687778519428213077122390720220*F(n+1)^10*F(n)^6*n^6-130452259527528498175696058160*F(n+1)^9*F(n)^7*n^6-2921154724634833105979479920*F(n+1)^8*F(n)^8*n^6-55635863433565368075562440*F(n+1)^7*F(n)^9*n^6-1001768442555637475891172*F(n+1)^6*F(n)^10*n^6-18901721124615200848704*F(n+1)^5*F(n)^11*n^6-391186573240266580140*F(n+1)^4*F(n)^12*n^6-9657757534237427160*F(n+1)^3*F(n)^13*n^6-240526926728557560*F(n+1)^2*F(n)^14*n^6-8371574086874544*F(n+1)*F(n)^15*n^6-18546684763374702488678010261885742500*F(n+1)^15*F(n)*n^5-5640411064662771902783714800774710000*F(n+1)^14*F(n)^2*n^5-177826004451*F(n)^16)/F(n+1)^16 which is asymptotic to (1/6412155926227569580078125)*(5317812500000000*n^24*r^16+450844143750000000*n^23*r^16+669406237500000000*n^23*r^15+3243526614453125000*n^22*r^16+68918850000000000*n^23*r^14+5215019184375000000*n^22*r^15-377084235812972187500*n^21*r^16+45945900000000000*n^23*r^13-9681662615625000000*n^22*r^14-785362717772132500000*n^21*r^15+16370398776356811875000*n^20*r^16-1114188075000000000*n^22*r^13-348633191248216875000*n^21*r^14-15824890296891457031250*n^20*r^15+448416942547572100557500*n^19*r^16-1085471887500000000*n^22*r^12-104417890007681250000*n^21*r^13-3189444754834150312500*n^20*r^14-21214273514751570297500*n^19*r^15-13328391832715202418181500*n^18*r^16-8047688573925000000*n^21*r^12+311733672396083437500*n^20*r^13+133862318540519547712500*n^19*r^14+5796081013364056320432750*n^18*r^15-239580123205926135485189490*n^17*r^16+6442492746690000000*n^21*r^11+1146578634015658593750*n^20*r^12+115172866862476292025000*n^19*r^13+6637571912887897516400250*n^18*r^14+189722662537696662801195000*n^17*r^15+3321937734993413610982079954*n^16*r^16+109415566260000000*n^21*r^10+113153280157417500000*n^20*r^11+16654391898920500725000*n^19*r^12+1251349578393093842422500*n^18*r^13+43674659937989435150657100*n^17*r^14+540365710674304905560310813*n^16*r^15+49204272973240383682201706440*n^15*r^16+31261590360000000*n^21*r^9-5890855933462500000*n^20*r^10-1681660315019354670000*n^19*r^11-280496112323699464042500*n^18*r^12-29990719268814337809084000*n^17*r^13-1929749043539055722736975030*n^16*r^14-58569680848119960352841001712*n^15*r^15-269544979308206642199158677540*n^14*r^16-36844017210000000*n^20*r^9-213404323633841340000*n^19*r^10-47221186906565683011000*n^18*r^11-6110171473501315561206600*n^17*r^12-507575164461291503474611680*n^16*r^13-24860403508269853910972856960*n^15*r^14-538879762271903566468338192420*n^14*r^15-2646779881638076149799589247700*n^13*r^16-173334353692500000*n^20*r^8-26665477850711700000*n^19*r^9-3361202715882490479000*n^18*r^10-267425553653962437880440*n^17*r^11-6213115762267577204888370*n^16*r^12+1327831385100944792354291160*n^15*r^13+163039826140810895333770068060*n^14*r^14+6392076581387047717742427876280*n^13*r^15-8857542835811959943111663454730*n^12*r^16-2424193980533325000*n^19*r^8-279580443979658679000*n^18*r^9-10888733071914078654000*n^17*r^10+2317589197478696227565304*n^16*r^11+543097043236111366405708920*n^15*r^12+58630475576211875398534072680*n^14*r^13+3490678195042824973674696329280*n^13*r^14+87644120887559713663725983559180*n^12*r^15-336931090383805725697602094204680*n^11*r^16+238297054945950000*n^19*r^7+31339173054260857500*n^18*r^8+5048835444078786968400*n^17*r^9+698721598471069090525608*n^16*r^10+75810047221822342277388960*n^15*r^11+5949705650775575896055998440*n^14*r^12+286684313936648494980702120480*n^13*r^13+4620606094460209072677401473920*n^12*r^14-146938320005529289324298544423480*n^11*r^15+2340842665679205154193962849103750*n^10*r^16+3979153858680000*n^19*r^6+4412406843872527500*n^18*r^7+702301013506608516000*n^17*r^8+89579643833962309182480*n^16*r^9+8842385050552229622585048*n^15*r^10+618600124377616787406728280*n^14*r^11+21021868694545639018324557660*n^13*r^12-983391534843379201487555995140*n^12*r^13-151436514632423552411333185580940*n^11*r^14-5213149371139593882219726524164860*n^10*r^15+47044302139599728039308429927990000*n^9*r^16+723482519760000*n^19*r^5+41324417175541500*n^18*r^6+20390440905981174600*n^17*r^7+2088656735961344993730*n^16*r^8+103146913637720881376760*n^15*r^9-10252332275905247865688260*n^14*r^10-3084602118725214536161369860*n^13*r^11-386106370444349946848011736610*n^12*r^12-28793588810602475296601099774280*n^11*r^13-1177198309326452217775359739062570*n^10*r^14-17730540391064566594114653801223750*n^9*r^15-109726220905550260703115110484240625*n^8*r^16+7619586355836000*n^18*r^5-404896061991872880*n^17*r^6-127740550880053927530*n^16*r^7-30290791927086352593360*n^15*r^8-4973885394397063337054160*n^14*r^9-627329754675958510246117320*n^13*r^10-60486545323346835485967141240*n^12*r^11-4205998339531337837818021475160*n^11*r^12-180807697226509500933140190907500*n^10*r^13-2742398111191334855917749140240100*n^9*r^14+56539126367879051199048673038345000*n^8*r^15-1910251647052047815841266081541752500*n^7*r^16-1021096919934000*n^18*r^4-68533291065798000*n^17*r^5-15053867558109712332*n^16*r^6-2217106235708399383920*n^15*r^7-281315991877239015676980*n^14*r^8-29290294334449848640875480*n^13*r^9-2310445326895720017612123060*n^12*r^10-109910234470101551394187505616*n^11*r^11+940814839707581904303886078860*n^10*r^12+621920482364518517283255219740400*n^9*r^13+44191408302516311449828044327663750*n^8*r^14+1102136302619279137033341806475940000*n^7*r^15+1722672741333132871359708163994928750*n^6*r^16-16768187246046600*n^17*r^4-1447419234329203824*n^16*r^5-150018958192260282840*n^15*r^6-13261435403754178194840*n^14*r^7-824677431688594099095480*n^13*r^8-3445345860262251687186120*n^12*r^9+8412334352524853696098645128*n^11*r^10+1423065923677233665038396713240*n^10*r^11+141096689736589347497425144942200*n^9*r^12+8914967099245578552677788451585400*n^8*r^13+317823827434435103017484984164650000*n^7*r^14+4355233493754829078679685907824922500*n^6*r^15+26198162972329876039477660388644968750*n^5*r^16+266373109548000*n^17*r^3-98324530106722920*n^16*r^4-7263892238155346664*n^15*r^5-495285582714658292700*n^14*r^6-16471650020235053503860*n^13*r^7+2360323191110459892521490*n^12*r^8+586837679908165336488422520*n^11*r^9+75122916972905419968726944568*n^10*r^10+6486615278207385436866439157040*n^9*r^11+356235755339493431648257747279050*n^8*r^12+7992633762437730587682931213290000*n^7*r^13-308098541995271174118787738119832500*n^6*r^14-18546684763374702488678010261885742500*n^5*r^15-5936964086449963156117459268419734375*n^4*r^16+7903377975600*n^17*r^2+4573523839743180*n^16*r^3-134566367481458640*n^15*r^4+1958446697978721600*n^14*r^5+1441739854145495464560*n^13*r^6+255920661272221487401860*n^12*r^7+31572118966179322269598860*n^11*r^8+2852820075244959755538740280*n^10*r^9+163839985431288200318197433520*n^9*r^10+521698398415822028530894950900*n^8*r^11-1032683347960934470483863196949400*n^7*r^12-111667953242056690000307304635220000*n^6*r^13-5640411064662771902783714800774710000*n^5*r^14-113726483677900127230031822235402093750*n^4*r^15-53238031937247218217112791018746718750*n^3*r^16+1053783730080*n^17*r+137255330842920*n^16*r^2+35586559525247640*n^15*r^3+1289930873059040940*n^14*r^4+159967097575276314960*n^13*r^5+16538883259116399281100*n^12*r^6+1510217603791039354634280*n^11*r^7+108705050612225335490211990*n^10*r^8+4491417923999665176996775440*n^9*r^9-186421214005590704244004981080*n^8*r^10-54842152691259199110801088917720*n^7*r^11-5182646784576587454958002579802500*n^6*r^12-257307429211999840003033079908200000*n^5*r^13-4753752335257582623265949498817712500*n^4*r^14+64942723601288507785687955308100250000*n^3*r^15-10454394698850358495620080051085140625*n^2*r^16+16491715375752*n^16*r+1106209470651480*n^15*r^2+165441674609167320*n^14*r^3+8269286368852929420*n^13*r^4+701991345723227469000*n^12*r^5+50974850957099766284016*n^11*r^6+2907133430499850561958520*n^10*r^7+60268827009503013069824370*n^9*r^8-12140931124132805136510019080*n^8*r^9-1954033025996622430220370216480*n^7*r^10-151843121867779342080981878643120*n^6*r^11-5281076934627514269546656155635000*n^5*r^12+151916484809039039315503324562475000*n^4*r^13+22391018153115704318110413550216500000*n^3*r^14+629333505062483350880740590226888031250*n^2*r^15-300686453987669129889318302523801703125*n*r^16-177826004451*n^16+118550669634000*n^15*r+5401431954457560*n^14*r^2+504183918469533120*n^13*r^3+23114871090249382080*n^12*r^4+1324917683670926823192*n^11*r^5+44251584252563622217140*n^10*r^6-2279546777233477387504440*n^9*r^7-632160288026496654559721730*n^8*r^8-69632573134592985184000518120*n^7*r^9-4687778519428213077122390720220*n^6*r^10-141097921077609626592472053772500*n^5*r^11+6784668081081273905805286375987500*n^4*r^12+896632217742281286812695050057975000*n^3*r^13+31092793420158771524772563644139250000*n^2*r^14+106271675911686957467184982209881812500*n*r^15-2845216071216*n^15+515827135874160*n^14*r+17520998634107640*n^13*r^2+1015586548207817040*n^12*r^3+31138195189073427000*n^11*r^4+210895865631344136672*n^10*r^5-154839104375590517814360*n^9*r^6-22509104379591534164434260*n^8*r^7-2075844125661796778655612960*n^7*r^8-130452259527528498175696058160*n^6*r^9-4197412284601890567380424369840*n^5*r^10+125577188646254541213893006580000*n^4*r^11+21255354385249689225359715351825000*n^3*r^12+827592943396753998719703211203000000*n^2*r^13+494339679648469866247962946367625000*n*r^14-366261688053916490438684313481857234375*r^15-21339120534120*n^14+1501114923498960*n^13*r+38669384313083160*n^12*r^2+1186327271876259240*n^11*r^3-7412758307639144460*n^10*r^4-5012103025985330555280*n^9*r^5-600887504110628296787940*n^8*r^6-49546093237378582681877040*n^7*r^7-2921154724634833105979479920*n^6*r^8-93390290619983998807855857480*n^5*r^9+2348215376538213202206102052500*n^4*r^10+456910674695700267906460876725000*n^3*r^11+21158488177323714082708814639587500*n^2*r^12+197752533754422733629023998656000000*n*r^13-8514081307850300182456066910112750000*r^14-99582562492560*n^13+3020671062274320*n^12*r+55259101575732600*n^11*r^2+32455787577693480*n^10*r^3-124893879958218391020*n^9*r^4-13536741285695139403320*n^8*r^5-1017308372905644168131640*n^7*r^6-55635863433565368075562440*n^6*r^7-1658120366187393121961333100*n^5*r^8+48772710155320709796215335800*n^4*r^9+9090897330923785899317381040000*n^3*r^10+484781741238488740401362877045000*n^2*r^11+9858731477652484987716733507312500*n*r^12-30911338175407147612004343823125000*r^13-323643328100820*n^12+4094687439971856*n^11*r+36354221458097400*n^10*r^2-3036818600175119760*n^9*r^3-289071979537695714360*n^8*r^4-19855020809215137457080*n^7*r^5-1001768442555637475891172*n^6*r^6-28409440947376083013479060*n^5*r^7+788017336290491179842233550*n^4*r^8+151235710229646240563640015000*n^3*r^9+8796775961140745813429774580000*n^2*r^10+240021702840940628965343421570000*n*r^11+1819931949732654543856392771750000*r^12-776743987441968*n^11+3089167004729520*n^10*r-40799608123439880*n^9*r^2-7086076106313564360*n^8*r^3-402892048748708850240*n^7*r^4-18901721124615200848704*n^6*r^5-546810268585514835021120*n^5*r^6+6724513404012243509712900*n^4*r^7+2003603702349225844497930300*n^3*r^8+125600285571730800081369300000*n^2*r^9+3925271917551853536406178895000*n*r^10+46965293085997890324141722437500*r^11-1424030643643608*n^10-678109830306480*n^9*r-153591876564417720*n^8*r^2-9854497161308119320*n^7*r^3-391186573240266580140*n^6*r^4-11961233531147270929104*n^5*r^5-70626367438052799061260*n^4*r^6+20143676433485811136530600*n^3*r^7+1443155510185185655298261250*n^2*r^8+49042555910806054256370360000*n*r^9+692763240275892177648910290000*r^10-2034329490919440*n^9-5575569715853280*n^8*r-237074731228815480*n^7*r^2-9657757534237427160*n^6*r^3-275167673033957203500*n^5*r^4-4758643914399958850280*n^4*r^5+118212077431603790949600*n^3*r^6+13307645143390486011680700*n^2*r^7+497789780428544870042741250*n*r^8+7680180645156504060981405000*r^9-2288620677284370*n^8-8664736720582800*n^7*r-240526926728557560*n^6*r^2-6951091533050115360*n^5*r^3-140626538633210862960*n^4*r^4-928690148391943724280*n^3*r^5+88234594216009355022480*n^2*r^6+4169478313959338160495000*n*r^7+69771657109086702004950000*r^8-2034329490919440*n^7-8371574086874544*n^6*r-174455740636271640*n^5*r^2-3683174726314072080*n^4*r^3-51091634786859674280*n^3*r^4+65448475892987728320*n^2*r^5+26978129619175706451480*n*r^6+532763199259954071873750*r^7-1424030643643608*n^6-5705712006518160*n^5*r-91875978628552440*n^4*r^2-1404973969882557480*n^3*r^3-12531855461117412420*n^2*r^4+72069678282739812480*n*r^5+3266182622659632390000*r^6-776743987441968*n^5-2814129451178640*n^4*r-34549089928470360*n^3*r^2-366281671746168360*n^2*r^3-1861595979280734060*n*r^4+10827233155293314760*r^5-323643328100820*n^4-991083598140240*n^3*r-8832551779598040*n^2*r^2-58550585299380720*n*r^3-126436660178053680*r^4-99582562492560*n^3-237628231133040*n^2*r-1379666348607240*n*r^2-4335222357893700*r^3-21339120534120*n^2-34880241465648*n*r-99582562492560*r^2-2845216071216*n-2371013392680*r-177826004451)/r^16 The limit of the standardized moment is, 2027025 In short, the first, 16, standardized central moments of X_n limit to [0, 1, 0, 3, 0, 15, 0, 105, 0, 945, 0, 10395, 0, 135135, 0, 2027025] And hence, X_n appears asymptotically normal. The computation time was, 23.263, seconds.