A218436 Sum of the 9th powers of the numbers of standard Young tableaux over all partitions of n.

1, 1, 2, 514, 39880, 14508236, 71502130216, 159891388498192, 515576952451247744, 3043225095505808401540, 113662467332884035859383856, 3902474169746657778866025106136, 123694078552827146016863752849997152, 3719080702866914288727567048533259759664

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=9 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)^9, `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]^9, 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 *)