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A295086 Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(3*k-1)/2). 4

%I #29 Nov 15 2017 09:09:02

%S 1,-1,-4,-8,1,24,78,111,75,-249,-876,-1847,-2251,-871,5170,17052,

%T 34742,47176,34576,-44016,-224561,-530104,-875149,-1030871,-475480,

%U 1488315,5658668,12109163,19411024,22693048,12926630,-24000623,-102605376,-230257606,-386964449

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

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

%H Seiichi Manyama, <a href="/A295086/b295086.txt">Table of n, a(n) for n = 0..10000</a>

%F Convolution inverse of A294102.

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

%F 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).

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

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

%K sign

%O 0,3

%A _Seiichi Manyama_, Nov 15 2017

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