A372182 E.g.f. A(x) satisfies A(x) = exp( x * A(x)^5 * (1 + x * A(x)^2) ).
1, 1, 13, 334, 13329, 724316, 49939411, 4177202562, 411049275265, 46530896718520, 5957142774561531, 851104158600401366, 134246582420467536289, 23171656877102178017028, 4344395473350526080895843, 879206880413471231912831626, 191028062860784640128743389441
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Keywords
Programs
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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!);
Formula
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!.