A218435 Sum of the 8th powers of the numbers of standard Young tableaux over all partitions of n.

1, 1, 2, 258, 13380, 2591940, 4582623240, 4616028796680, 6229088692170120, 15072293332114590600, 159846322935857039370000, 1733855206389212577000330000, 17554952499518858027710809780000, 183908030642450770233388352642100000

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=8 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)^8, `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]^8, 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 *)