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%I #13 Nov 15 2017 09:13:47
%S 1,-1,-5,-10,3,42,124,160,15,-677,-1941,-3425,-2807,3488,21004,49547,
%T 77879,63395,-65104,-406091,-988889,-1655508,-1779329,-145347,5087175,
%U 15405270,30158849,42617486,36116136,-19457047,-161973496,-418712896,-759063566
%N Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(2*k-1)).
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n*(2*n-1), g(n) = -1.
%H Seiichi Manyama, <a href="/A295121/b295121.txt">Table of n, a(n) for n = 0..10000</a>
%F Convolution inverse of A294836.
%F G.f.: Product_{k>=1} 1/(1 + x^k)^A000384(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*(2*d-1)*(-1)^(n/d).
%o (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+x^k)^(k*(2*k-1))))
%Y Cf. A294846 (b=3), A284896 (b=4), A295086 (b=5), this sequence (b=6), A295122 (b=7), A295123 (b=8).
%K sign
%O 0,3
%A _Seiichi Manyama_, Nov 15 2017
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