A361532 Expansion of e.g.f. exp((x + x^2/2)/(1-x)).

1, 1, 4, 19, 118, 886, 7786, 78184, 881644, 11017108, 150966856, 2249261356, 36181351504, 624658612384, 11516406883528, 225740649754936, 4686671645814736, 102712289940757264, 2369128149877075264, 57359541280704038128, 1454229915957292684576

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = (2*n-1) * a(n-1) - (n-1)*(n-3) * a(n-2) - binomial(n-1,2) * a(n-3) for n > 2.

a(n) ~ 2^(-3/4) * 3^(1/4) * exp(-5/4 + sqrt(6*n) - n) * n^(n - 1/4) * (1 + sqrt(3)/(2*sqrt(2*n))). - Vaclav Kotesovec, Mar 20 2023

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[(x+x^2/2)/(1-x)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 08 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x+x^2/2)/(1-x))))

Crossrefs

Cf. A361548, A361557, A361558.

Cf. A052845, A112242, A185369.

Sequence in context: A163859 A197660 A354458 * A094822 A280939 A121125

Adjacent sequences: A361529 A361530 A361531 * A361533 A361534 A361535

Keyword

nonn

Author

Seiichi Manyama, Mar 15 2023

Status

approved