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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..60

Wikipedia, Young tableau

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 *)

Crossrefs

Column k=9 of A208447.

Sequence in context: A320520 A196290 A182446 * A080778 A007513 A352852

Adjacent sequences: A218433 A218434 A218435 * A218437 A218438 A218439

Keyword

nonn

Author

Alois P. Heinz, Oct 28 2012

Status

approved