A372179 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) / (1 - x * A(x)) ).

1, 2, 12, 134, 2232, 49762, 1394236, 47117982, 1866217296, 84810000194, 4350808646964, 248736339576958, 15682868019616408, 1081153176108929250, 80906410246285190508, 6531880775140905838238, 565912845564569155284384, 52373575389612727174282882

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A365012.

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!.

Prog

(PARI) a(n, r=2, s=1, t=1, 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!);

Crossrefs

Cf. A365012, A372165, A372178.

Sequence in context: A077696 A326361 A117271 * A289998 A180353 A208873

Adjacent sequences: A372176 A372177 A372178 * A372180 A372181 A372182

Keyword

nonn

Author

Seiichi Manyama, Apr 21 2024

Status

approved