A295123 Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(3*k-2)).

1, -1, -7, -14, 10, 93, 242, 229, -410, -2446, -5500, -6458, 4062, 38899, 104715, 165843, 103045, -327200, -1393131, -3075317, -4305200, -2069461, 9129361, 35219829, 75832840, 109569915, 74818084, -143480059, -686408279, -1607860793, -2614721006, -2674073316

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-2), g(n) = -1.

Links

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

Crossrefs

Cf. A294846 (b=3), A284896 (b=4), A295086 (b=5), A295121 (b=6), A295122 (b=7), this sequence (b=8).

Programs

PARI

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

Formula

Convolution inverse of A294838.

G.f.: Product_{k>=1} 1/(1 + x^k)^A000567(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*(3*d-2)*(-1)^(n/d).