A380917 - OEIS

%I #7 Feb 08 2025 10:29:55

%S 1,4,31,453,9957,293103,10850625,484699491,25381819737,1525299702363,

%T 103484966417109,7824985701013143,652582573442231733,

%U 59509330659228595239,5890961096785803165129,629159786981753244521787,72111288184913038638092337,8828896697592792281849882547

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

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

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

%Y Cf. A380914, A380916.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 08 2025