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A295086 Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(3*k-1)/2). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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).

PROG

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

CROSSREFS

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

Sequence in context: A294830 A248415 A328250 * A331331 A134484 A244641

Adjacent sequences:  A295083 A295084 A295085 * A295087 A295088 A295089

KEYWORD

sign

AUTHOR

Seiichi Manyama, Nov 15 2017

STATUS

approved

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Last modified January 23 01:30 EST 2020. Contains 331166 sequences. (Running on oeis4.)