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

0,3

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)^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 *)

Crossrefs

Column k=8 of A208447.

Sequence in context: A196288 A128697 A182422 * A089663 A252708 A103029

Adjacent sequences: A218432 A218433 A218434 * A218436 A218437 A218438

Keyword

nonn

Author

Alois P. Heinz, Oct 28 2012

Status

approved