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 A285131 #21 Apr 16 2017 10:27:03 %S A285131 1,0,0,3,0,0,6,7,0,10,21,11,15,42,61,36,70,150,150,124,278,441,375, %T A285131 468,909,1131,1018,1581,2602,2810,2947,4819,6768,6980,8509,13389, %U A285131 16788,17609,23722,34720,40337,44863,63128,85430,95887,114037,159882,202699,227087 %N A285131 Expansion of Product_{k>=0} 1/(1-x^(4*k+3))^(4*k+3). %H A285131 Seiichi Manyama, <a href="/A285131/b285131.txt">Table of n, a(n) for n = 0..10000</a> %F A285131 a(n) ~ exp(4*c + 3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(11/72) / (2^(47/72) * sqrt(3) * Gamma(3/4) * n^(47/72)), where c = Integral_{x=0..inf} ((5/(exp(x)*96) + 1/(exp(3*x)*(1 - exp(-4*x))^2) - 1/(16*x^2) - 1/(16*x))/x) dx = -0.158924147180165035059952001737321408554746599955833696821824808... - _Vaclav Kotesovec_, Apr 15 2017 %t A285131 nmax = 100; CoefficientList[Series[Product[1/(1-x^(4*k+3))^(4*k+3), {k,0,nmax}], {x,0,nmax}], x] (* _Vaclav Kotesovec_, Apr 15 2017 *) %o A285131 (PARI) x='x+O('x^100); Vec(prod(k=0, 100, 1/(1 - x^(4*k + 3))^(4*k + 3))) \\ _Indranil Ghosh_, Apr 15 2017 %Y A285131 Product_{k>=0} 1/(1-x^(m*k+m-1))^(m*k+m-1): A262811 (m=2), A262946 (m=3), this sequence (m=4), A285132 (m=5). %Y A285131 Cf. A285213. %K A285131 nonn %O A285131 0,4 %A A285131 _Seiichi Manyama_, Apr 15 2017