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 A385067 #11 Jun 17 2025 03:33:44
%S A385067 1,1,2,3,5,6,8,11,14,18,23,30,38,47,58,71,87,106,128,154,185,221,263,
%T A385067 313,370,437,514,603,705,822,958,1112,1289,1491,1721,1982,2279,2617,
%U A385067 2999,3432,3921,4473,5095,5795,6583,7468,8461,9574,10820,12214,13772,15512,17453
%N A385067 G.f.: Sum_{k>=0} x^k * Product_{j=1..3*k} (1 + x^j).
%H A385067 Vaclav Kotesovec, <a href="/A385067/b385067.txt">Table of n, a(n) for n = 0..5000</a>
%F A385067 a(n) ~ Gamma(1/3) * exp(Pi*sqrt(n/3)) / (2^(4/3) * 3^(11/12) * Pi^(2/3) * n^(5/12)).
%t A385067 nmax = 60; CoefficientList[Series[Sum[x^k*Product[1 + x^j, {j, 1, 3*k}], {k, 0, nmax}], {x, 0, nmax}], x]
%t A385067 nmax = 60; p = 1; s = 1; Do[p = Expand[p*(1 + x^(3*k))*(1 + x^(3*k - 1))*(1 + x^(3*k - 2))]; 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 A385067 Cf. A000009, A192433, A385068, A385069, A385070.
%Y A385067 Cf. A035295.
%K A385067 nonn
%O A385067 0,3
%A A385067 _Vaclav Kotesovec_, Jun 16 2025