A319607 Sum of the n-th powers of the numbers of standard Young tableaux over all partitions of n.

1, 1, 2, 10, 180, 16076, 19902600, 134324703472, 6229088692170120, 3043225095505808401540, 82539616591562766578923554000, 20307821456335470464284341150217960760, 48436056178178689690954566323758042309244664480

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..41

Wikipedia, Young tableau

Formula

a(n) = A208447(n,n).

Maple

h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(j>
    l[k], 0, 1), k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):
g:= (n, i, k, l)-> `if`(n=0 or i=1, h([l[], 1$n])^k,
    g(n, i-1, k, l)+g(n-i, min(i, n-i), k, [l[], i])):
a:= n-> g(n$3, []):
seq(a(n), n=0..15);

Crossrefs

Main diagonal of A208447.

Sequence in context: A368573 A356887 A086675 * A057119 A226563 A037267

Adjacent sequences: A319604 A319605 A319606 * A319608 A319609 A319610

Keyword

nonn

Author

Alois P. Heinz, Sep 24 2018

Status

approved