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

0,3

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)^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 *)

Crossrefs

Column k=7 of A208447.

Sequence in context: A190578 A098533 A182421 * A354054 A303445 A158110

Adjacent sequences: A218431 A218432 A218433 * A218435 A218436 A218437

Keyword

nonn

Author

Alois P. Heinz, Oct 28 2012

Status

approved