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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 (list; graph; refs; listen; history; text; internal format)
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: A069994 A063573 A086675 * A057119 A226563 A037267

Adjacent sequences:  A319604 A319605 A319606 * A319608 A319609 A319610

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 24 2018

STATUS

approved

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Last modified May 11 15:11 EDT 2021. Contains 343791 sequences. (Running on oeis4.)