A377889 - OEIS

%I #9 Nov 11 2024 06:47:01

%S 1,2,21,472,16581,795736,48509641,3589729760,312603962985,

%T 31321633489408,3549706188092541,448973808123051520,

%U 62697159481460439469,9581292408000225087488,1590488540940006100524657,284993765391981838318575616,54826610288277007690469896017

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

%F a(n) = n! * Sum_{k=0..n} (3*n-2*k+1)^(k-1) * binomial(4*n-3*k,n-k)/k!.

%o (PARI) a(n) = n!*sum(k=0, n, (3*n-2*k+1)^(k-1)*binomial(4*n-3*k, n-k)/k!);

%Y Cf. A352410, A377831, A377888.

%Y Cf. A373324.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 10 2024