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

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