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A261648 Expansion of Product_{k>=0} ((1+x^(2*k+1))/(1-x^(2*k+1)))^5. 4

%I

%S 1,10,50,180,550,1512,3820,9040,20310,43670,90472,181540,354180,

%T 674040,1254640,2289104,4101430,7228020,12546030,21473940,36281656,

%U 60565920,99974140,163297520,264110180,423211938,672244600,1059013320,1655274320,2568068120

%N Expansion of Product_{k>=0} ((1+x^(2*k+1))/(1-x^(2*k+1)))^5.

%C In general, if j > 0 and g.f. = Product_{k>=0} ((1 + x^(2*k+1))/(1 - x^(2*k+1)))^j, then a(n) ~ exp(Pi*sqrt(j*n/2)) * j^(1/4) / (2^(j/2 + 7/4) * n^(3/4)).

%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. 11.

%F a(n) ~ exp(Pi*sqrt(5*n/2)) * 5^(1/4) / (16 * 2^(1/4) * n^(3/4)).

%t nmax=60; CoefficientList[Series[Product[((1+x^(2*k+1))/(1-x^(2*k+1)))^5,{k,0,nmax}],{x,0,nmax}],x]

%Y Cf. A080054 (j=1), A007096 (j=2), A261647 (j=3), A014969 (j=4), A014970 (j=6), A014972 (j=8), A103261 (j=10).

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 28 2015

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Last modified March 28 14:53 EDT 2020. Contains 333089 sequences. (Running on oeis4.)