#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
]]]: