A218433 Sum of the 6th powers of the numbers of standard Young tableaux over all partitions of n.

1, 1, 2, 66, 1524, 86100, 19902600, 3965056200, 976304082600, 384973061999400, 347437227718904400, 365434181398477976400, 390696545168036224840800, 475968229571639505471170400, 784642922815221782474131569600, 2070759893211522247088843511422400

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)^6, `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]^6, 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=6 of A208447.

Sequence in context: A157060 A154637 A069865 * A092884 A230735 A361884

Adjacent sequences: A218430 A218431 A218432 * A218434 A218435 A218436

Keyword

nonn

Author

Alois P. Heinz, Oct 28 2012

Status

approved