A298985 a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^k)^k.

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

Vaclav Kotesovec, Table of n, a(n) for n = 0..380

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}]

Crossrefs

Cf. A000219, A124577, A261561, A261565, A266941, A297329, A298986, A298987, A298988.

Sequence in context: A002775 A079754 A347274 * A142703 A138403 A013499

Adjacent sequences: A298982 A298983 A298984 * A298986 A298987 A298988

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2018

Status

approved