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A319607
Sum of the n-th powers of the numbers of standard Young tableaux over all partitions of n.
2
1, 1, 2, 10, 180, 16076, 19902600, 134324703472, 6229088692170120, 3043225095505808401540, 82539616591562766578923554000, 20307821456335470464284341150217960760, 48436056178178689690954566323758042309244664480
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 24 2018
STATUS
approved