

A295086


Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(3*k1)/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
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OFFSET

0,3


COMMENTS

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n*(3*n1)/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(nk) where b(n) = Sum_{dn} d^2*(3*d1)*(1)^(n/d).


PROG

(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+x^k)^(k*(3*k1)/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



