A218437 Sum of the 10th powers of the numbers of standard Young tableaux over all partitions of n.

1, 1, 2, 1026, 119124, 82094580, 1126524259080, 5563004909321160, 43453047082604239080, 620787527477497337506920, 82539616591562766578923554000, 8875098123308028836585309148354000, 891186933432311275150434427455009708000

Offset: 0

Author

Alois P. Heinz, Oct 28 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..60
• Wikipedia, Young tableau

Crossrefs

Column k=10 of A208447.

Programs

Maple

h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j
       +add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
    end:
g:= proc(n, i, l) `if`(n=0, h(l)^10, `if`(i<1, 0, g(n, i-1, l)+
      `if`(i>n, 0, g(n-i, i, [l[], i]))))
    end:
a:= n-> `if`(n=0, 1, g(n, n, [])):
seq(a(n), n=0..20);

Mathematica

h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, l_] := g[n, i, l] = If[n == 0, h[l]^10, If[i < 1, 0, g[n, i - 1, l] + If[i > n, 0, g[n - i, i, Append[l, i]]]]];
a[n_] := If[n == 0, 1, g[n, n, {}]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 18 2017, translated from Maple *)