A380047 - OEIS

%I #8 Jan 11 2025 10:26:35

%S 1,3,12,45,132,135,-702,6573,111576,-634581,-19482690,104641713,

%T 5438689380,-21226768017,-2173847986086,3249084663765,

%U 1168505502268848,2167390942251219,-807540016560944778,-5035872168333504807,693302551375611396540,8209523136574257223383

%N E.g.f. A(x) satisfies A(x) = 1 + 3*x*exp(x)*A(x)^(1/3).

%F E.g.f.: B(x)^3, where B(x) is the e.g.f. of A380051.

%F a(n) = n! * Sum_{k=0..n} 3^k * k^(n-k) * binomial(k/3+1,k)/( (k/3+1)*(n-k)! ).

%o (PARI) a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(k/3+1, k)/((k/3+1)*(n-k)!));

%Y Cf. A006153, A380046.

%Y Cf. A380051.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jan 11 2025