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 A385088 #11 Jun 18 2025 07:34:52
%S A385088 1,1,3,7,13,23,39,63,101,159,243,367,547,801,1161,1665,2359,3315,4621,
%T A385088 6385,8761,11941,16165,21757,29121,38761,51337,67673,88793,116009,
%U A385088 150949,195629,252595,324987,416675,532483,678333,861489,1090913,1377553,1734761,2178883
%N A385088 G.f.: Sum_{k>=0} x^k * Product_{j=1..2*k} (1 + x^j)/(1 - x^j).
%H A385088 Vaclav Kotesovec, <a href="/A385088/b385088.txt">Table of n, a(n) for n = 0..5000</a>
%F A385088 a(n) ~ exp(Pi*sqrt(n)) / (16 * n^(3/4)).
%t A385088 nmax = 50; CoefficientList[Series[Sum[x^k*Product[(1+x^j)/(1-x^j), {j, 1, 2*k}], {k, 0, nmax}], {x, 0, nmax}], x]
%t A385088 nmax = 50; p = 1; q = 1; s = 1; Do[p = Expand[p*(1 - x^(2*k))*(1 - x^(2*k - 1))]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; q = Expand[q*(1 + x^(2*k))*(1 + x^(2*k - 1))]; q = Take[q, Min[nmax + 1, Exponent[q, x] + 1, Length[q]]]; s += x^k*q/p;, {k, 1, nmax}]; CoefficientList[Series[s, {x, 0, nmax}], x]
%Y A385088 Cf. A035294, A192433.
%Y A385088 Cf. A207641, A385089, A385090, A385091, A385092.
%K A385088 nonn
%O A385088 0,3
%A A385088 _Vaclav Kotesovec_, Jun 17 2025