A361548 Expansion of e.g.f. exp((x + x^2/2 + x^3/6)/(1-x)).

1, 1, 4, 20, 126, 966, 8656, 88544, 1016380, 12920156, 179996816, 2725070096, 44521522024, 780344770440, 14599772973696, 290311643773376, 6112190642062096, 135798496839920144, 3174483084427144000, 77872118431269176896, 1999809157085214044896

Offset: 0

Author

Seiichi Manyama, Mar 15 2023

Keywords

• nonn

Crossrefs

Cf. A361532, A361557, A361558.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[(x+x^2/2+x^3/6)/(1-x)],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 03 2024 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x+x^2/2+x^3/6)/(1-x))))

Formula

a(n) = (2*n-1) * a(n-1) - (n-1)*(n-3) * a(n-2) - 2*binomial(n-1,3) * a(n-4) for n > 3.