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URL: https://oeis.org/A298985

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A298985
a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^k)^k.
5
1, 1, 8, 54, 496, 5400, 73728, 1204322, 23167808, 512093178, 12781430600, 355128859129, 10863077554224, 362572265689777, 13107541496092960, 510105773344747725, 21258690342206888192, 944467894258279964254, 44555341678790400325512, 2224158766859058600584834, 117123916650423288611260400
OFFSET
0,3
LINKS
FORMULA
a(n) ~ n^n. - Vaclav Kotesovec, Feb 02 2018
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(i+j-1, j)*b(n-i*j, i-1, k)*k^j, j=0..n/i)))
end:
a:= n-> b(n$3):
seq(a(n), n=0..30); # Alois P. Heinz, Sep 23 2018
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1 - n x^k)^k, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2018
STATUS
approved