A334562 E.g.f.: exp(-(x + x^2 + x^3)).

1, -1, -1, -1, 25, 19, -209, -2269, 2801, 68615, 371071, -2499641, -28306871, -58645861, 1964456495, 15133179179, -37119981599, -1861550428529, -9225044407169, 110317002942095, 2150185424201081, 3953685082287779, -233260896605772881, -2920858244957587661, 7649165533910291665

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 A334561.

Cf. A118589, A334569.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[-(x+x^2+x^3)],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Nov 26 2020 *)

PARI

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

Formula

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

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