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 A386203 #8 Jul 15 2025 08:29:26
%S A386203 1,1,1,1,1,2,7,22,57,184,949,4984,21649,99728,659443,4777648,29500593,
%T A386203 179618176,1441372201,13153104256,105727977601,808208897792,
%U A386203 7631709900607,83311277669632,825548919414057,7638849184574464,83126488334117149,1050853652511099904
%N A386203 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * a(4*k) * a(n-1-4*k).
%F A386203 E.g.f. A(x) satisfies A'(x) = A(x) * (A(x) + A(i*x) + A(-x) + A(-i*x))/4, where i is the imaginary unit.
%o A386203 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\4, binomial(i-1, 4*j)*v[4*j+1]*v[i-4*j])); v;
%Y A386203 Cf. A000111, A000142, A386202.
%Y A386203 Cf. A118968, A385725.
%K A386203 nonn
%O A386203 0,6
%A A386203 _Seiichi Manyama_, Jul 14 2025