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 A385068 #12 Jun 17 2025 03:34:21
%S A385068 1,1,2,3,5,7,9,12,16,20,26,33,41,52,65,81,99,121,147,177,214,255,304,
%T A385068 362,429,507,596,700,820,959,1119,1301,1510,1750,2023,2335,2688,3089,
%U A385068 3546,4062,4647,5306,6050,6889,7833,8895,10085,11422,12921,14599,16477,18573,20914
%N A385068 G.f.: Sum_{k>=0} x^k * Product_{j=1..4*k} (1 + x^j).
%H A385068 Vaclav Kotesovec, <a href="/A385068/b385068.txt">Table of n, a(n) for n = 0..5000</a>
%F A385068 a(n) ~ Gamma(1/4) * 3^(1/8) * exp(Pi*sqrt(n/3)) / (2^(13/4) * Pi^(3/4) * n^(3/8)).
%t A385068 nmax = 60; CoefficientList[Series[Sum[x^k*Product[1 + x^j, {j, 1, 4*k}], {k, 0, nmax}], {x, 0, nmax}], x]
%t A385068 nmax = 60; p = 1; s = 1; Do[p = Expand[p*(1 + x^(4*k))*(1 + x^(4*k - 1))*(1 + x^(4*k - 2))*(1 + x^(4*k - 3))]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p*x^k;, {k, 1, nmax}]; CoefficientList[Series[s, {x, 0, nmax}], x]
%Y A385068 Cf. A000009, A192433, A385067, A385069, A385070.
%Y A385068 Cf. A035296.
%K A385068 nonn
%O A385068 0,3
%A A385068 _Vaclav Kotesovec_, Jun 16 2025