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A218435 Sum of the 8th powers of the numbers of standard Young tableaux over all partitions of n. 2
1, 1, 2, 258, 13380, 2591940, 4582623240, 4616028796680, 6229088692170120, 15072293332114590600, 159846322935857039370000, 1733855206389212577000330000, 17554952499518858027710809780000, 183908030642450770233388352642100000 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified February 27 12:22 EST 2020. Contains 332306 sequences. (Running on oeis4.)