%I #8 Apr 21 2024 11:40:46

%S 1,1,13,340,13713,752516,52372051,4421017602,438996446545,

%T 50142716621848,6477138263806011,933667525669154486,

%U 148582199464010331289,25874197258988478298068,4894174597530612144797299,999256176035969437218129946,219035687330062179838536993441

%N E.g.f. A(x) satisfies A(x) = exp( x * A(x)^5 / (1 - x * A(x)^2) ).

%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=1, s=1, t=5, u=2) = 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. A212722, A361093, A365012.

%Y Cf. A372165.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 21 2024