A295086 Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(3*k-1)/2).

1, -1, -4, -8, 1, 24, 78, 111, 75, -249, -876, -1847, -2251, -871, 5170, 17052, 34742, 47176, 34576, -44016, -224561, -530104, -875149, -1030871, -475480, 1488315, 5658668, 12109163, 19411024, 22693048, 12926630, -24000623, -102605376, -230257606, -386964449

Offset: 0

Author

Seiichi Manyama, Nov 15 2017

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n*(3*n-1)/2, g(n) = -1.

Links

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

Crossrefs

Cf. A294846 (b=3), A284896 (b=4), this sequence (b=5), A295121 (b=6), A295122 (b=7), A295123 (b=8).

Programs

PARI

N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+x^k)^(k*(3*k-1)/2)))

Formula

Convolution inverse of A294102.

G.f.: Product_{k>=1} 1/(1 + x^k)^A000326(k).

a(0) = 1 and a(n) = (1/(2*n)) * Sum_{k=1..n} b(k)*a(n-k) where b(n) = Sum_{d|n} d^2*(3*d-1)*(-1)^(n/d).