A385990 - OEIS

%I #6 Jul 14 2025 10:03:02

%S 1,2,14,250,10762,1160726,334178342,269864173450,629119441422346,

%T 4300094237465965718,86926579696107616781126,

%U 5223854240144609158089474250,936213967612878042630582862931818,501401563584674616157299481286097996374,803517566423095869415868021817376896171061478

%N 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 E.g.f. A(x) satisfies A'(x) = A(x) * (A(2*x) + A(3*x)).

%o (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 Cf. A385620.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 14 2025