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%I #15 Feb 13 2024 11:40:37
%S 1,-1,0,-1,2,-2,1,-2,4,-4,3,-4,8,-8,6,-9,14,-14,12,-16,24,-25,22,-28,
%T 40,-42,38,-48,65,-68,64,-78,102,-108,104,-124,159,-168,164,-194,242,
%U -256,254,-296,362,-385,386,-444,536,-570,576,-658,782,-832,848,-961
%N Expansion of Product_{k>=1} (1 + x^(4*k))/(1 + x^k).
%H Seiichi Manyama, <a href="/A261734/b261734.txt">Table of n, a(n) for n = 0..10000</a>
%H David J. Hemmer, <a href="https://arxiv.org/abs/2402.03643">Generating functions for fixed points of the Mullineux map</a>, arXiv:2402.03643 [math.CO], 2024.
%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 14.
%F a(n) ~ (-1)^n * exp(sqrt(n)*Pi/2) / (4*sqrt(2)*n^(3/4)).
%p seq(coeff(series(mul((1+x^(4*k))/(1+x^k),k=1..n), x,n+1),x,n),n=0..60); # _Muniru A Asiru_, Jul 29 2018
%t nmax = 100; CoefficientList[Series[Product[(1 + x^(4*k))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A081360 (m=2), A109389 (m=3), A133563 (m=5), A261736 (m=6), A113297 (m=7), A261735 (m=8), A261733 (m=9), A145707 (m=10).
%K sign
%O 0,5
%A _Vaclav Kotesovec_, Aug 30 2015