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 A035295 #18 Jul 08 2025 21:31:51
%S A035295 1,1,2,4,7,11,17,26,38,54,77,107,148,201,272,363,483,635,832,1081,
%T A035295 1399,1796,2299,2924,3707,4673,5874,7348,9166,11384,14102,17404,21425,
%U A035295 26285,32172,39259,47799,58036,70318,84985,102507,123354,148163,177582,212464,253692,302411
%N A035295 Expansion of sum ( q^n / product( 1-q^k, k=1..3*n), n=0..inf ).
%H A035295 Vaclav Kotesovec, <a href="/A035295/b035295.txt">Table of n, a(n) for n = 0..5000</a>
%F A035295 a(n) ~ Gamma(1/3) * exp(Pi*sqrt(2*n/3)) / (2^(5/3) * 3^(7/6) * Pi^(2/3) * n^(2/3)). - _Vaclav Kotesovec_, Jun 16 2025
%t A035295 nmax = 50; CoefficientList[Series[Sum[x^k/Product[1 - x^j, {j, 1, 3*k}], {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 16 2025 *)
%t A035295 nmax = 50; 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+=x^k/p;, {k, 1, nmax}]; CoefficientList[Series[s, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 16 2025 *)
%Y A035295 Cf. A363066, A385067.
%K A035295 nonn
%O A035295 0,3
%A A035295 _N. J. A. Sloane_
%E A035295 More terms from _Vaclav Kotesovec_, Jun 16 2025