This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A262364 #32 Mar 22 2018 06:01:44
%S A262364 1,0,1,0,2,-1,3,-1,5,-2,6,-3,10,-5,13,-7,19,-11,25,-15,35,-22,45,-30,
%T A262364 62,-41,79,-55,105,-75,134,-98,175,-130,220,-168,284,-219,355,-280,
%U A262364 451,-360,561,-455,705,-578,870,-725,1085,-910,1331,-1132,1644,-1410
%N A262364 Expansion of Product_{k>=1} (1-x^(5*k))/(1-x^(2*k)).
%C A262364 In general, if m >= 1 and g.f. = Product_{k>=1} (1-x^((2*m+1)*k))/(1-x^(2*k)), then a(n) ~ (-1)^n * exp(Pi*sqrt((4*m+1)*n/(6*(2*m+1)))) * (4*m+1)^(1/4) / (2^(7/4) * 3^(1/4) * (2*m+1)^(3/4) * n^(3/4)).
%H A262364 Vaclav Kotesovec, <a href="/A262364/b262364.txt">Table of n, a(n) for n = 0..5000</a>
%H A262364 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], 2015-2016, p. 15.
%F A262364 a(n) ~ (-1)^n * 3^(1/4) * exp(Pi*sqrt(3*n/10)) / (2^(7/4) * 5^(3/4) * n^(3/4)).
%e A262364 G.f. = 1 + x^2 + 2*x^4 - x^5 + 3*x^6 - x^7 + 5*x^8 - 2*x^9 + ...
%t A262364 nmax = 60; CoefficientList[Series[Product[(1-x^(5*k))/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x]
%t A262364 CoefficientList[Series[QPochhammer[x^5]/QPochhammer[x^2], {x, 0, 60}], x]
%o A262364 (PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q^5)/eta(q^2))} \\ _Altug Alkan_, Mar 21 2018
%Y A262364 Cf. A035959, A147783, A262346.
%K A262364 sign
%O A262364 0,5
%A A262364 _Vaclav Kotesovec_, Sep 23 2015