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 A309240 #8 Jul 17 2019 16:38:37
%S A309240 1,1,2,1,1,1,3,3,4,2,4,4,7,5,7,6,11,9,13,10,17,14,20,15,25,22,32,24,
%T A309240 36,31,48,38,55,45,68,55,79,65,97,79,112,91,136,113,159,128,186,156,
%U A309240 221,179,256,213,301,245,347,290,409,334,466,388,547,451,624,517,724,600,828,687,955,793,1088
%N A309240 Expansion of 1/((1 - x)*(1 - x^2)*(1 + x^3)*(1 + x^4)*(1 - x^5)*(1 - x^6)*(1 + x^7)*(1 + x^8)*...).
%H A309240 Vaclav Kotesovec, <a href="/A309240/b309240.txt">Table of n, a(n) for n = 0..10000</a>
%F A309240 G.f.: Product_{k>=1} 1/(1 + (-1)^(k*(k+1)/2) * x^k).
%F A309240 G.f.: Product_{k>=1} (1 + x^(4*k-2)) / ((1 + x^(4*k-1)) * (1 - x^(4*k-3))).
%F A309240 a(n) ~ Gamma(1/4) * exp(Pi*sqrt(n/6)) / (4 * 6^(1/8) * Pi^(3/4) * n^(5/8)). - _Vaclav Kotesovec_, Jul 17 2019
%t A309240 nmax = 70; CoefficientList[Series[Product[1/(1 + (-1)^(k (k + 1)/2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A309240 nmax = 70; CoefficientList[Series[Product[(1 + x^(4 k - 2))/((1 + x^(4 k - 1)) (1 - x^(4 k - 3))), {k, 1, nmax}], {x, 0, nmax}], x]
%t A309240 nmax = 70; CoefficientList[Series[2/(QPochhammer[-1, -x^2] QPochhammer[x, -x^2]), {x, 0, nmax}], x]
%Y A309240 Cf. A000700, A035451, A147599, A300574.
%K A309240 nonn
%O A309240 0,3
%A A309240 _Ilya Gutkovskiy_, Jul 17 2019