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%I #10 Sep 24 2018 14:11:00
%S 1,1,2,10,180,16076,19902600,134324703472,6229088692170120,
%T 3043225095505808401540,82539616591562766578923554000,
%U 20307821456335470464284341150217960760,48436056178178689690954566323758042309244664480
%N Sum of the n-th powers of the numbers of standard Young tableaux over all partitions of n.
%H Alois P. Heinz, <a href="/A319607/b319607.txt">Table of n, a(n) for n = 0..41</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F a(n) = A208447(n,n).
%p h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(j>
%p l[k], 0, 1), k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):
%p g:= (n, i, k, l)-> `if`(n=0 or i=1, h([l[], 1$n])^k,
%p g(n, i-1, k, l)+g(n-i, min(i, n-i), k, [l[], i])):
%p a:= n-> g(n$3, []):
%p seq(a(n), n=0..15);
%Y Main diagonal of A208447.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 24 2018
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