#This is the 6 times 6 times 6 list-of-lists-of-lists, called here SBmoms such that #SBmoms[i+1][j+1][k+1] is the (i,j,k)-mixed moment #of the Sucker Bets statistics with three decks, each with n cards, and all the 3n cards have different numbers #See the article http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/suckerbets.html SBmoms:= [[[1, 0, 1/3*n^2*(2*n+1), 0, 1/15*n^3*(2*n+1)*(10*n^2-n-4), 0], [0, -1/3*n^3, 0 , -1/15*n^4*(10*n^2-n-4), 0, -1/63*n^4*(140*n^5-112*n^4-115*n^3+92*n^2+32*n-16) ], [1/3*n^2*(2*n+1), 0, 1/45*n^3*(30*n^3+14*n^2+3*n-2), 0, 1/315*n^3*(560*n^6-\ 112*n^5-146*n^4-3*n^3-16*n^2+40*n-8), 0], [0, -1/15*n^4*(10*n^2-n-4), 0, -1/315 *n^3*(490*n^6-210*n^5-357*n^4+42*n^3+144*n^2-12*n+8), 0, -1/945*n^3*(5600*n^9-\ 8120*n^8-2406*n^7+6237*n^6+3060*n^5-3336*n^4-1664*n^3+1280*n^2-432*n+96)], [1/ 15*n^3*(2*n+1)*(10*n^2-n-4), 0, 1/315*n^3*(560*n^6-112*n^5-146*n^4-3*n^3-16*n^2 +40*n-8), 0, 1/4725*n^3*(26600*n^9-31920*n^8-2568*n^7+26472*n^6-7899*n^5-6480*n ^4+3928*n^3-5232*n^2+2304*n-480), 0], [0, -1/63*n^4*(140*n^5-112*n^4-115*n^3+92 *n^2+32*n-16), 0, -1/945*n^3*(5600*n^9-8120*n^8-2406*n^7+6237*n^6+3060*n^5-3336 *n^4-1664*n^3+1280*n^2-432*n+96), 0, -1/6237*n^3*(157080*n^12-437360*n^11+ 261624*n^10+333608*n^9-301281*n^8-162960*n^7-47736*n^6+254240*n^5+44928*n^4-\ 183584*n^3+119808*n^2-44352*n+8064)]], [[0, -1/3*n^3, 0, -1/15*n^4*(10*n^2-n-4) , 0, -1/63*n^4*(140*n^5-112*n^4-115*n^3+92*n^2+32*n-16)], [-1/3*n^3, 0, -1/45*n ^3*(11*n^2+2*n+2), 0, 1/315*n^3*(140*n^6-420*n^5-13*n^4+144*n^3+12*n^2+40*n-8), 0], [0, -1/45*n^3*(11*n^2+2*n+2), 0, -1/315*n^3*(70*n^6+28*n^5+45*n^4-52*n^3+34 *n^2-28*n+8), 0, -1/945*n^3*(1400*n^9-2800*n^8+2588*n^7-861*n^6+226*n^5-102*n^4 -760*n^3+1024*n^2-496*n+96)], [-1/15*n^4*(10*n^2-n-4), 0, -1/315*n^3*(70*n^6+28 *n^5+45*n^4-52*n^3+34*n^2-28*n+8), 0, 1/4725*n^3*(1400*n^9-7560*n^8-1350*n^7+ 6507*n^6+2472*n^5-4908*n^4+4768*n^3-4680*n^2+2256*n-480), 0], [0, 1/315*n^3*( 140*n^6-420*n^5-13*n^4+144*n^3+12*n^2+40*n-8), 0, 1/4725*n^3*(1400*n^9-7560*n^8 -1350*n^7+6507*n^6+2472*n^5-4908*n^4+4768*n^3-4680*n^2+2256*n-480), 0, -1/31185 *n^3*(46200*n^12-141680*n^11+330352*n^10-151580*n^9-423201*n^8+479004*n^7-\ 127692*n^6-171016*n^5+574328*n^4-774688*n^3+552960*n^2-222912*n+40320)], [-1/63 *n^4*(140*n^5-112*n^4-115*n^3+92*n^2+32*n-16), 0, -1/945*n^3*(1400*n^9-2800*n^8 +2588*n^7-861*n^6+226*n^5-102*n^4-760*n^3+1024*n^2-496*n+96), 0, -1/31185*n^3*( 46200*n^12-141680*n^11+330352*n^10-151580*n^9-423201*n^8+479004*n^7-127692*n^6-\ 171016*n^5+574328*n^4-774688*n^3+552960*n^2-222912*n+40320), 0]], [[1/3*n^2*(2* n+1), 0, 1/45*n^3*(30*n^3+14*n^2+3*n-2), 0, 1/315*n^3*(560*n^6-112*n^5-146*n^4-\ 3*n^3-16*n^2+40*n-8), 0], [0, -1/45*n^3*(11*n^2+2*n+2), 0, -1/315*n^3*(70*n^6+ 28*n^5+45*n^4-52*n^3+34*n^2-28*n+8), 0, -1/945*n^3*(1400*n^9-2800*n^8+2588*n^7-\ 861*n^6+226*n^5-102*n^4-760*n^3+1024*n^2-496*n+96)], [1/45*n^3*(30*n^3+14*n^2+3 *n-2), 0, 1/315*n^3*(140*n^6+294*n^5-72*n^4-9*n^3-54*n^2+24*n-8), 0, 1/4725*n^3 *(5600*n^9+8120*n^8-8686*n^7-5874*n^6+6475*n^5-3390*n^4+5216*n^3-4496*n^2+2240* n-480), 0], [0, -1/315*n^3*(70*n^6+28*n^5+45*n^4-52*n^3+34*n^2-28*n+8), 0, -1/ 4725*n^3*(2800*n^9+3290*n^8-9918*n^7+5757*n^6-3516*n^5+6594*n^4-5776*n^3+4072*n ^2-2208*n+480), 0, -1/31185*n^3*(92400*n^12-33880*n^11-435402*n^10+626956*n^9-\ 90681*n^8-204888*n^7+191454*n^6-465956*n^5+727464*n^4-744976*n^3+529920*n^2-\ 222336*n+40320)], [1/315*n^3*(560*n^6-112*n^5-146*n^4-3*n^3-16*n^2+40*n-8), 0, 1/4725*n^3*(5600*n^9+8120*n^8-8686*n^7-5874*n^6+6475*n^5-3390*n^4+5216*n^3-4496 *n^2+2240*n-480), 0, 1/155925*n^3*(462000*n^12+773080*n^11-2399408*n^10+1100176 *n^9+447582*n^8+1099791*n^7-2867640*n^6+3347384*n^5-3910048*n^4+3818240*n^3-\ 2599968*n^2+1086336*n-201600), 0], [0, -1/945*n^3*(1400*n^9-2800*n^8+2588*n^7-\ 861*n^6+226*n^5-102*n^4-760*n^3+1024*n^2-496*n+96), 0, -1/31185*n^3*(92400*n^12 -33880*n^11-435402*n^10+626956*n^9-90681*n^8-204888*n^7+191454*n^6-465956*n^5+ 727464*n^4-744976*n^3+529920*n^2-222336*n+40320), 0, -1/2837835*n^3*(33633600*n ^15-12612600*n^14-364283920*n^13+823446624*n^12-371158944*n^11-572235067*n^10+ 516766182*n^9+110459702*n^8-578801744*n^7+1443895728*n^6-2642784288*n^5+ 3369542272*n^4-3039561984*n^3+1848398464*n^2-675202560*n+111444480)]], [[0, -1/ 15*n^4*(10*n^2-n-4), 0, -1/315*n^3*(490*n^6-210*n^5-357*n^4+42*n^3+144*n^2-12*n +8), 0, -1/945*n^3*(5600*n^9-8120*n^8-2406*n^7+6237*n^6+3060*n^5-3336*n^4-1664* n^3+1280*n^2-432*n+96)], [-1/15*n^4*(10*n^2-n-4), 0, -1/315*n^3*(70*n^6+28*n^5+ 45*n^4-52*n^3+34*n^2-28*n+8), 0, 1/4725*n^3*(1400*n^9-7560*n^8-1350*n^7+6507*n^ 6+2472*n^5-4908*n^4+4768*n^3-4680*n^2+2256*n-480), 0], [0, -1/315*n^3*(70*n^6+ 28*n^5+45*n^4-52*n^3+34*n^2-28*n+8), 0, -1/4725*n^3*(2800*n^9+3290*n^8-9918*n^7 +5757*n^6-3516*n^5+6594*n^4-5776*n^3+4072*n^2-2208*n+480), 0, -1/31185*n^3*( 92400*n^12-33880*n^11-435402*n^10+626956*n^9-90681*n^8-204888*n^7+191454*n^6-\ 465956*n^5+727464*n^4-744976*n^3+529920*n^2-222336*n+40320)], [-1/315*n^3*(490* n^6-210*n^5-357*n^4+42*n^3+144*n^2-12*n+8), 0, -1/4725*n^3*(2800*n^9+3290*n^8-\ 9918*n^7+5757*n^6-3516*n^5+6594*n^4-5776*n^3+4072*n^2-2208*n+480), 0, -1/51975* n^3*(141680*n^11+80014*n^10-716342*n^9+899763*n^8-842358*n^7+1120788*n^6-\ 1397660*n^5+1433408*n^4-1258768*n^3+849024*n^2-359424*n+67200), 0], [0, 1/4725* n^3*(1400*n^9-7560*n^8-1350*n^7+6507*n^6+2472*n^5-4908*n^4+4768*n^3-4680*n^2+ 2256*n-480), 0, -1/51975*n^3*(141680*n^11+80014*n^10-716342*n^9+899763*n^8-\ 842358*n^7+1120788*n^6-1397660*n^5+1433408*n^4-1258768*n^3+849024*n^2-359424*n+ 67200), 0, -1/14189175*n^3*(42042000*n^15+29429400*n^14-288648360*n^13+ 454726272*n^12-616876650*n^11+1522875611*n^10-3466829696*n^9+6088185732*n^8-\ 9388493136*n^7+13388708088*n^6-16915309920*n^5+17936178880*n^4-15034561408*n^3+ 9035218560*n^2-3339138048*n+557222400)], [-1/945*n^3*(5600*n^9-8120*n^8-2406*n^ 7+6237*n^6+3060*n^5-3336*n^4-1664*n^3+1280*n^2-432*n+96), 0, -1/31185*n^3*( 92400*n^12-33880*n^11-435402*n^10+626956*n^9-90681*n^8-204888*n^7+191454*n^6-\ 465956*n^5+727464*n^4-744976*n^3+529920*n^2-222336*n+40320), 0, -1/14189175*n^3 *(42042000*n^15+29429400*n^14-288648360*n^13+454726272*n^12-616876650*n^11+ 1522875611*n^10-3466829696*n^9+6088185732*n^8-9388493136*n^7+13388708088*n^6-\ 16915309920*n^5+17936178880*n^4-15034561408*n^3+9035218560*n^2-3339138048*n+ 557222400), 0]], [[1/15*n^3*(2*n+1)*(10*n^2-n-4), 0, 1/315*n^3*(560*n^6-112*n^5 -146*n^4-3*n^3-16*n^2+40*n-8), 0, 1/4725*n^3*(26600*n^9-31920*n^8-2568*n^7+ 26472*n^6-7899*n^5-6480*n^4+3928*n^3-5232*n^2+2304*n-480), 0], [0, 1/315*n^3*( 140*n^6-420*n^5-13*n^4+144*n^3+12*n^2+40*n-8), 0, 1/4725*n^3*(1400*n^9-7560*n^8 -1350*n^7+6507*n^6+2472*n^5-4908*n^4+4768*n^3-4680*n^2+2256*n-480), 0, -1/31185 *n^3*(46200*n^12-141680*n^11+330352*n^10-151580*n^9-423201*n^8+479004*n^7-\ 127692*n^6-171016*n^5+574328*n^4-774688*n^3+552960*n^2-222912*n+40320)], [1/315 *n^3*(560*n^6-112*n^5-146*n^4-3*n^3-16*n^2+40*n-8), 0, 1/4725*n^3*(5600*n^9+ 8120*n^8-8686*n^7-5874*n^6+6475*n^5-3390*n^4+5216*n^3-4496*n^2+2240*n-480), 0, 1/155925*n^3*(462000*n^12+773080*n^11-2399408*n^10+1100176*n^9+447582*n^8+ 1099791*n^7-2867640*n^6+3347384*n^5-3910048*n^4+3818240*n^3-2599968*n^2+1086336 *n-201600), 0], [0, 1/4725*n^3*(1400*n^9-7560*n^8-1350*n^7+6507*n^6+2472*n^5-\ 4908*n^4+4768*n^3-4680*n^2+2256*n-480), 0, -1/51975*n^3*(141680*n^11+80014*n^10 -716342*n^9+899763*n^8-842358*n^7+1120788*n^6-1397660*n^5+1433408*n^4-1258768*n ^3+849024*n^2-359424*n+67200), 0, -1/14189175*n^3*(42042000*n^15+29429400*n^14-\ 288648360*n^13+454726272*n^12-616876650*n^11+1522875611*n^10-3466829696*n^9+ 6088185732*n^8-9388493136*n^7+13388708088*n^6-16915309920*n^5+17936178880*n^4-\ 15034561408*n^3+9035218560*n^2-3339138048*n+557222400)], [1/4725*n^3*(26600*n^9 -31920*n^8-2568*n^7+26472*n^6-7899*n^5-6480*n^4+3928*n^3-5232*n^2+2304*n-480), 0, 1/155925*n^3*(462000*n^12+773080*n^11-2399408*n^10+1100176*n^9+447582*n^8+ 1099791*n^7-2867640*n^6+3347384*n^5-3910048*n^4+3818240*n^3-2599968*n^2+1086336 *n-201600), 0, 1/23648625*n^3*(140140000*n^15+504504000*n^14-1499618120*n^13-\ 1096791696*n^12+7342193508*n^11-10641870640*n^10+11263147417*n^9-15566404476*n^ 8+22207220072*n^7-27552084528*n^6+31164782784*n^5-30989982368*n^4+25030908160*n ^3-14872399872*n^2+5518608384*n-928704000), 0], [0, -1/31185*n^3*(46200*n^12-\ 141680*n^11+330352*n^10-151580*n^9-423201*n^8+479004*n^7-127692*n^6-171016*n^5+ 574328*n^4-774688*n^3+552960*n^2-222912*n+40320), 0, -1/14189175*n^3*(42042000* n^15+29429400*n^14-288648360*n^13+454726272*n^12-616876650*n^11+1522875611*n^10 -3466829696*n^9+6088185732*n^8-9388493136*n^7+13388708088*n^6-16915309920*n^5+ 17936178880*n^4-15034561408*n^3+9035218560*n^2-3339138048*n+557222400), 0, -1/ 2837835*n^3*(39239200*n^18+66146080*n^17-816055240*n^16+1114633520*n^15+ 3208398492*n^14-13589761044*n^13+25028291837*n^12-38043392560*n^11+62580129596* n^10-103184180072*n^9+157753326632*n^8-224678523360*n^7+293133737664*n^6-\ 336053442624*n^5+322828696448*n^4-243844376832*n^3+132045454336*n^2-44452356096 *n+6864979968)]], [[0, -1/63*n^4*(140*n^5-112*n^4-115*n^3+92*n^2+32*n-16), 0, -\ 1/945*n^3*(5600*n^9-8120*n^8-2406*n^7+6237*n^6+3060*n^5-3336*n^4-1664*n^3+1280* n^2-432*n+96), 0, -1/6237*n^3*(157080*n^12-437360*n^11+261624*n^10+333608*n^9-\ 301281*n^8-162960*n^7-47736*n^6+254240*n^5+44928*n^4-183584*n^3+119808*n^2-\ 44352*n+8064)], [-1/63*n^4*(140*n^5-112*n^4-115*n^3+92*n^2+32*n-16), 0, -1/945* n^3*(1400*n^9-2800*n^8+2588*n^7-861*n^6+226*n^5-102*n^4-760*n^3+1024*n^2-496*n+ 96), 0, -1/31185*n^3*(46200*n^12-141680*n^11+330352*n^10-151580*n^9-423201*n^8+ 479004*n^7-127692*n^6-171016*n^5+574328*n^4-774688*n^3+552960*n^2-222912*n+ 40320), 0], [0, -1/945*n^3*(1400*n^9-2800*n^8+2588*n^7-861*n^6+226*n^5-102*n^4-\ 760*n^3+1024*n^2-496*n+96), 0, -1/31185*n^3*(92400*n^12-33880*n^11-435402*n^10+ 626956*n^9-90681*n^8-204888*n^7+191454*n^6-465956*n^5+727464*n^4-744976*n^3+ 529920*n^2-222336*n+40320), 0, -1/2837835*n^3*(33633600*n^15-12612600*n^14-\ 364283920*n^13+823446624*n^12-371158944*n^11-572235067*n^10+516766182*n^9+ 110459702*n^8-578801744*n^7+1443895728*n^6-2642784288*n^5+3369542272*n^4-\ 3039561984*n^3+1848398464*n^2-675202560*n+111444480)], [-1/945*n^3*(5600*n^9-\ 8120*n^8-2406*n^7+6237*n^6+3060*n^5-3336*n^4-1664*n^3+1280*n^2-432*n+96), 0, -1 /31185*n^3*(92400*n^12-33880*n^11-435402*n^10+626956*n^9-90681*n^8-204888*n^7+ 191454*n^6-465956*n^5+727464*n^4-744976*n^3+529920*n^2-222336*n+40320), 0, -1/ 14189175*n^3*(42042000*n^15+29429400*n^14-288648360*n^13+454726272*n^12-\ 616876650*n^11+1522875611*n^10-3466829696*n^9+6088185732*n^8-9388493136*n^7+ 13388708088*n^6-16915309920*n^5+17936178880*n^4-15034561408*n^3+9035218560*n^2-\ 3339138048*n+557222400), 0], [0, -1/31185*n^3*(46200*n^12-141680*n^11+330352*n^ 10-151580*n^9-423201*n^8+479004*n^7-127692*n^6-171016*n^5+574328*n^4-774688*n^3 +552960*n^2-222912*n+40320), 0, -1/14189175*n^3*(42042000*n^15+29429400*n^14-\ 288648360*n^13+454726272*n^12-616876650*n^11+1522875611*n^10-3466829696*n^9+ 6088185732*n^8-9388493136*n^7+13388708088*n^6-16915309920*n^5+17936178880*n^4-\ 15034561408*n^3+9035218560*n^2-3339138048*n+557222400), 0, -1/2837835*n^3*( 39239200*n^18+66146080*n^17-816055240*n^16+1114633520*n^15+3208398492*n^14-\ 13589761044*n^13+25028291837*n^12-38043392560*n^11+62580129596*n^10-\ 103184180072*n^9+157753326632*n^8-224678523360*n^7+293133737664*n^6-\ 336053442624*n^5+322828696448*n^4-243844376832*n^3+132045454336*n^2-44452356096 *n+6864979968)], [-1/6237*n^3*(157080*n^12-437360*n^11+261624*n^10+333608*n^9-\ 301281*n^8-162960*n^7-47736*n^6+254240*n^5+44928*n^4-183584*n^3+119808*n^2-\ 44352*n+8064), 0, -1/2837835*n^3*(33633600*n^15-12612600*n^14-364283920*n^13+ 823446624*n^12-371158944*n^11-572235067*n^10+516766182*n^9+110459702*n^8-\ 578801744*n^7+1443895728*n^6-2642784288*n^5+3369542272*n^4-3039561984*n^3+ 1848398464*n^2-675202560*n+111444480), 0, -1/2837835*n^3*(39239200*n^18+ 66146080*n^17-816055240*n^16+1114633520*n^15+3208398492*n^14-13589761044*n^13+ 25028291837*n^12-38043392560*n^11+62580129596*n^10-103184180072*n^9+ 157753326632*n^8-224678523360*n^7+293133737664*n^6-336053442624*n^5+ 322828696448*n^4-243844376832*n^3+132045454336*n^2-44452356096*n+6864979968), 0 ]]]: