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E.g.f. A(x) satisfies A(x) = exp( x * A(x)^5 * (1 + x * A(x)^2) ).
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%I #7 Apr 21 2024 11:40:49

%S 1,1,13,334,13329,724316,49939411,4177202562,411049275265,

%T 46530896718520,5957142774561531,851104158600401366,

%U 134246582420467536289,23171656877102178017028,4344395473350526080895843,879206880413471231912831626,191028062860784640128743389441

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

%Y Cf. A143768, A363355, A363358.

%Y Cf. A372164.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 21 2024