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

Author

Alois P. Heinz, Sep 24 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..41
• Wikipedia, Young tableau

Crossrefs

Main diagonal of A208447.

Programs

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);

Formula

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