A372201 - OEIS

%I #7 Apr 22 2024 07:19:44

%S 1,3,27,351,6309,145143,4083669,136159299,5256248265,230783968395,

%T 11364265672929,620524946670687,37222254648712989,2433741005377774719,

%U 172301622840992025117,13133140607475128862747,1072406955985984437773841,93406430850089038192704915

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

%F E.g.f.: A(x) = B(x)^3 where B(x) is the e.g.f. of A364938.

%F If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.

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

%Y Cf. A161630, A372200.

%Y Cf. A364938.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 21 2024