A294953 Expansion of Product_{k>=1} (1 - k^(2*k)*x^k)^k.

1, -1, -32, -2155, -259701, -48496253, -13001952944, -4732375549802, -2246504006429898, -1348407213767476321, -998562531571744073815, -894380298523142455736017, -953030939828900988652689704, -1191547999931410291515116161158

Offset: 0

Author

Seiichi Manyama, Nov 12 2017

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -n, g(n) = n^(2*n).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..213

Crossrefs

Column k=2 of A294808.

Cf. A294954, A294955.

Programs

PARI

N=20; x='x+O('x^N); Vec(prod(k=1, N, (1-k^(2*k)*x^k)^k))

Formula

a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} A294955(k)*a(n-k) for n > 0.