A295121 Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(2*k-1)).

1, -1, -5, -10, 3, 42, 124, 160, 15, -677, -1941, -3425, -2807, 3488, 21004, 49547, 77879, 63395, -65104, -406091, -988889, -1655508, -1779329, -145347, 5087175, 15405270, 30158849, 42617486, 36116136, -19457047, -161973496, -418712896, -759063566

Offset

0,3

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n*(2*n-1), g(n) = -1.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

Convolution inverse of A294836.

G.f.: Product_{k>=1} 1/(1 + x^k)^A000384(k).

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} b(k)*a(n-k) where b(n) = Sum_{d|n} d^2*(2*d-1)*(-1)^(n/d).

Prog

(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+x^k)^(k*(2*k-1))))

Crossrefs

Cf. A294846 (b=3), A284896 (b=4), A295086 (b=5), this sequence (b=6), A295122 (b=7), A295123 (b=8).

Sequence in context: A169841 A084341 A054513 * A066200 A357913 A053822

Adjacent sequences: A295118 A295119 A295120 * A295122 A295123 A295124

Keyword

sign

Author

Seiichi Manyama, Nov 15 2017

Status

approved