A392566 Expansion of e.g.f. (1/x) * Series_Reversion( x*exp(-x*(3+x)) ).

1, 3, 29, 504, 12885, 438048, 18648273, 955478016, 57293930313, 3938025600000, 305336853105669, 26369255495467008, 2510493688261968669, 261252072029313662976, 29504344983796139765625, 3594050725647273953329152, 469749733096169195471535633, 65575342339459194563110895616

Offset

0,2

Links

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

Formula

E.g.f. A(x) satisfies A(x) = exp(3*x*A(x) + (x*A(x))^2).

a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-k-1) * 3^(n-2*k) * binomial(n-k,k)/(n-k)!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(-x*(3+x)))/x))

Crossrefs

Cf. A088695, A120590, A192949.

Sequence in context: A326433 A113871 A379862 * A377832 A380721 A380781

Adjacent sequences: A392563 A392564 A392565 * A392567 A392568 A392569

Keyword

nonn

Author

Seiichi Manyama, Mar 04 2026

Status

approved