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%I #29 Sep 08 2022 08:44:46
%S 1,5,15,40,95,206,425,835,1575,2880,5121,8885,15095,25165,41240,66562,
%T 105945,166480,258560,397235,604162,910325,1359680,2014235,2961000,
%U 4321283,6263360,9019555,12908945,18367805,25990149,36581200,51228175,71393555,99037095,136775685,188091960
%N Expansion of Product_{m>=1} (1+x^m)^5.
%H Seiichi Manyama, <a href="/A022570/b022570.txt">Table of n, a(n) for n = 0..1000</a>
%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. 8.
%F a(n) ~ (5/3)^(1/4) * exp(Pi * sqrt(5*n/3)) / (16 * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015
%F a(0) = 1, a(n) = (5/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 03 2017
%F G.f.: exp(5*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018
%t nmax=50; CoefficientList[Series[Product[(1+q^m)^5,{m,1,nmax}],{q,0,nmax}],q] (* _Vaclav Kotesovec_, Mar 05 2015 *)
%o (PARI) x='x+O('x^51); Vec(prod(m=1, 50, (1 + x^m)^5)) \\ _Indranil Ghosh_, Apr 03 2017
%o (Magma) Coefficients(&*[(1+x^m)^5:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 26 2018
%Y Cf. A000009.
%Y Column k=5 of A286335.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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