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A284896
Expansion of Product_{k>=1} 1/(1+x^k)^(k^2) in powers of x.
14
1, -1, -3, -6, 0, 11, 42, 63, 73, -45, -267, -720, -1095, -1239, -66, 2794, 8757, 16017, 22885, 19634, -2359, -61979, -161867, -302190, -421971, -432051, -126712, 690578, 2278273, 4584989, 7269985, 8965464, 7515373, -845659, -19930400, -53474765, -100195759
OFFSET
0,3
COMMENTS
This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n^2, g(n) = -1. - Seiichi Manyama, Nov 15 2017
LINKS
FORMULA
a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A078307(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 06 2017
G.f.: exp(Sum_{k>=1} (-1)^k*x^k*(1 + x^k)/(k*(1 - x^k)^3)). - Ilya Gutkovskiy, May 30 2018
MATHEMATICA
CoefficientList[Series[Product[1/(1 + x^k)^(k^2) , {k, 40}], {x, 0, 40}], x] (* Indranil Ghosh, Apr 05 2017 *)
PROG
(PARI) x= 'x + O('x^40); Vec(prod(k=1, 40, 1/(1 + x^k)^(k^2))) \\ Indranil Ghosh, Apr 05 2017
CROSSREFS
Product_{k>=1} 1/(1+x^k)^(k^m): A081362 (m=0), A255528 (m=1), this sequence (m=2), A284897 (m=3), A284898 (m=4), A284899 (m=5).
Sequence in context: A010618 A287845 A070297 * A299032 A094674 A125287
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 05 2017
STATUS
approved