A372177 E.g.f. A(x) satisfies A(x) = exp( x * A(x)^(1/2) * (1 + A(x)^(1/2)) ).
1, 2, 10, 86, 1072, 17652, 362692, 8950216, 258135136, 8525942000, 317455926544, 13159289478480, 601125054656320, 30006335335032448, 1625132762002203136, 94920040351049627648, 5947667725489120124416, 397991563599617527723776
Offset: 0
Keywords
Programs
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PARI
a(n, r=1, t=1/2, u=1/2) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
Formula
E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A138860.
If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + A(x)^(u/r)) ), then a(n) = r * Sum_{k=0..n} (t*n+u*k+r)^(n-1) * binomial(n,k).