A218434 Sum of the 7th powers of the numbers of standard Young tableaux over all partitions of n.

1, 1, 2, 130, 4504, 468956, 298313896, 134324703472, 76943411156480, 75584451935796484, 231249690461453112208, 784105479220668188046200, 2566797235899935973173794336, 9244479688068495046254956909968, 48983678227627955151056666560212512

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=7 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)^7, `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]^7, 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 *)