A372203 - OEIS

%I #9 Apr 22 2024 07:22:23

%S 1,3,27,297,4581,87363,2014389,54516969,1695624345,59673787587,

%T 2345478318369,101896766246817,4850500185441909,251143864572078819,

%U 14055460408215741069,845667848072862801657,54441943452534058086321,3734566046400701428294275

%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 A365030.

%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(s*k,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(s*k, n-k)/k!);

%Y Cf. A365030, A372201.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 21 2024