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 A386202 #9 Jul 15 2025 08:27:54
%S A386202 1,1,1,1,2,6,16,52,234,1018,4724,27864,166816,1018096,7421220,
%T A386202 56215420,427276280,3714931512,33908654224,309043657936,3126424467816,
%U A386202 33317327728936,354276443249552,4093007897140128,49813497858533344,605442506092221760,7871720463184084560
%N A386202 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(3*k) * a(n-1-3*k).
%F A386202 E.g.f. A(x) satisfies A'(x) = A(x) * (A(x) + A(w*x) + A(w^2*x))/3, where w = exp(2*Pi*i/3).
%o A386202 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, binomial(i-1, 3*j)*v[3*j+1]*v[i-3*j])); v;
%Y A386202 Cf. A000111, A000142, A386203.
%Y A386202 Cf. A124753, A385691.
%K A386202 nonn
%O A386202 0,5
%A A386202 _Seiichi Manyama_, Jul 14 2025