%I #9 Apr 21 2024 11:48:51

%S 1,3,15,117,1269,17763,305829,6264261,148974009,4037901219,

%T 122940227169,4155745911837,154473245377317,6263647154467875,

%U 275184369838089357,13023134386197318837,660560328648108969201,35751895401064184128707

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

%F E.g.f.: A(x) = B(x)^3 where B(x) is the e.g.f. of A161630.

%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=1, 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.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 20 2024