A334569 E.g.f.: exp(-(x + x^2/2 + x^3/3)).

1, -1, 0, 0, 6, -6, -24, -120, 540, 1764, 2016, -68256, -147960, 700920, 11870496, 5245344, -330495984, -2602348560, 6794046720, 141179998464, 619736321376, -6025074044256, -66284988059520, -87481563442560, 4660723755205056, 34028147176271424, -98057302990861824

Offset: 0

Author

Seiichi Manyama, May 06 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Column 3 of A334568.

Cf. A057693, A334562.

Programs

Mathematica

m = 25; Range[0, m]! * CoefficientList[Series[Exp[-(x + x^2/2 + x^3/3)], {x, 0, m}], x] (* Amiram Eldar, May 03 2021 *)

PARI

N=40; x='x+O('x^N); Vec(serlaplace(exp(-x-x^2/2-x^3/3)))

Formula

a(0) = 1 and a(n) = - (n-1)! * Sum_{k=1..min(3,n)} a(n-k)/(n-k)!.

D-finite with recurrence a(n) +a(n-1) +(n-1)*a(n-2) +(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, May 07 2020