A372165 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(5/2) / (1 - x * A(x)) ).
1, 2, 28, 758, 31160, 1730562, 121434364, 10312487054, 1028675082960, 117917384790914, 15275849114906804, 2207219937751153998, 351952462602081499480, 61392924661901606654402, 11629541557015551899838252, 2377438129669444985664704078, 521710054052646408966825988256
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, 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!);
Formula
E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A372183.
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!.