cp's OEIS Frontend

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.

A385990 a(0) = 1; a(n) = Sum_{k=0..n-1} (2^k + 3^k) * binomial(n-1,k) * a(k) * a(n-1-k).

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%I A385990 #6 Jul 14 2025 10:03:02
%S A385990 1,2,14,250,10762,1160726,334178342,269864173450,629119441422346,
%T A385990 4300094237465965718,86926579696107616781126,
%U A385990 5223854240144609158089474250,936213967612878042630582862931818,501401563584674616157299481286097996374,803517566423095869415868021817376896171061478
%N A385990 a(0) = 1; a(n) = Sum_{k=0..n-1} (2^k + 3^k) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A385990 E.g.f. A(x) satisfies A'(x) = A(x) * (A(2*x) + A(3*x)).
%o A385990 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (2^j+3^j)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385990 Cf. A385620.
%K A385990 nonn
%O A385990 0,2
%A A385990 _Seiichi Manyama_, Jul 14 2025