%I #12 Nov 15 2017 09:56:19

%S 1,-1,-7,-14,10,93,242,229,-410,-2446,-5500,-6458,4062,38899,104715,

%T 165843,103045,-327200,-1393131,-3075317,-4305200,-2069461,9129361,

%U 35219829,75832840,109569915,74818084,-143480059,-686408279,-1607860793,-2614721006,-2674073316

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

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

%H Seiichi Manyama, <a href="/A295123/b295123.txt">Table of n, a(n) for n = 0..10000</a>

%F Convolution inverse of A294838.

%F G.f.: Product_{k>=1} 1/(1 + x^k)^A000567(k).

%F 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).

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

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

%K sign

%O 0,3

%A _Seiichi Manyama_, Nov 15 2017