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 A363404 #17 Jun 01 2023 11:11:46
%S A363404 1,1,1,1,2,2,2,4,5,5,10,12,13,26,34,36,73,96,104,210,288,315,638,881,
%T A363404 974,1975,2777,3089,6276,8895,9970,20272,29000,32668,66508,95703,
%U A363404 108347,220771,319483,363141,740615,1076331,1227826,2505979,3655912,4183309,8544123,12504292,14347462
%N A363404 G.f. satisfies A(x) = exp( Sum_{k>=1} (A(x^k) + A(w*x^k) + A(w^2*x^k))/3 * x^k/k ), where w = exp(2*Pi*i/3).
%H A363404 Seiichi Manyama, <a href="/A363404/b363404.txt">Table of n, a(n) for n = 0..1000</a>
%F A363404 A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(3*k+1))^a(3*k).
%F A363404 A(x) * A(w*x) * A(w^2*x) = A(x^3).
%F A363404 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 3} d * a(d-1) ) * a(n-k).
%o A363404 (PARI) seq(n) = my(w=exp(2*Pi*I/3), A=1); for(i=1, n, A=exp(sum(k=1, i, sum(m=0, 2, subst(A, x, w^m*x^k))/3*x^k/k)+x*O(x^n))); apply(round, Vec(A));
%Y A363404 Cf. A195865, A363405.
%Y A363404 Cf. A363336.
%K A363404 nonn
%O A363404 0,5
%A A363404 _Seiichi Manyama_, May 31 2023