The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Nov 11 2024 06:49:01
%S 1,2,19,364,10665,423056,21221851,1288931456,91977076561,
%T 7543664425216,699290913249891,72306463481715200,8251192866018497401,
%U 1030074741274860240896,139650729116792108398891,20432888021354725476499456,3209204194084043665909835937,538542735919965101952197525504
%N E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * exp(x * A(x)).
%F a(n) = n! * Sum_{k=0..n} (3*n-2*k+1)^(k-1) * binomial(3*n-2*k+1,n-k)/k!.
%o (PARI) a(n) = n!*sum(k=0, n, (3*n-2*k+1)^(k-1)*binomial(3*n-2*k+1, n-k)/k!);
%Y Cf. A088690, A377826, A377890.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 11 2024