A334570 E.g.f.: exp(-(x + x^2/2 + x^3/3 + x^4/4)).

1, -1, 0, 0, 0, 24, -24, -120, -720, -5040, 32256, 169344, 743040, -380160, -91048320, -408710016, -174230784, 29842525440, 455765667840, 1061427732480, -18914141343744, -379628241094656, -3305984467691520, 10588546824468480, 458522651844956160, 5722461010387021824

Offset: 0

Author

Seiichi Manyama, May 06 2020

Keywords

• sign

Links

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

Crossrefs

Column 4 of A334568.

Cf. A070945, A334564.

Programs

Mathematica

m = 25; Range[0, m]! * CoefficientList[Series[Exp[-(x + x^2/2 + x^3/3 + x^4/4)], {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-x^4/4)))

Formula

a(0) = 1 and a(n) = - (n-1)! * Sum_{k=1..min(4,n)} a(n-k)/(n-k)!.