A334565 E.g.f.: exp(-(x + x^2 + x^3 + x^4 + x^5)).

1, -1, -1, -1, 1, 19, 871, 1091, -12319, -185401, -1871729, -16185401, 124125409, 2716194779, 30386265911, 192015557579, -1519087028159, -90118169425649, -1286566655151329, -8992926875821681, 96361313388009281, 5078872062174772259, 107995117552995689479, 996704518577739393619

Offset: 0

Author

Seiichi Manyama, May 06 2020

Keywords

• sign

Links

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

Crossrefs

Column 5 of A334561.

Cf. A193931, A334571.

Programs

Mathematica

m = 25; Range[0, m]! * CoefficientList[Series[Exp[-(x + x^2 + x^3 + x^4 + x^5)], {x, 0, m}], x] (* Amiram Eldar, May 03 2021 *)

PARI

N=40; x='x+O('x^N); Vec(serlaplace(exp(-x-x^2-x^3-x^4-x^5)))

Formula

a(0) = 1 and a(n) = - (n-1)! * Sum_{k=1..min(5,n)} k*a(n-k)/(n-k)!.