A334571 E.g.f.: exp(-(x + x^2/2 + x^3/3 + x^4/4 + x^5/5)).

1, -1, 0, 0, 0, 0, 120, -120, -720, -5040, -40320, -362880, 3024000, 21859200, 151113600, 753667200, -3978374400, -249882796800, -1752623308800, -7319841177600, 79100731699200, 2905096654540800, 48387220210944000, 226481995918080000, -2094278695939584000, -85503113536135680000

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 A334568.

Cf. A070946, A334565.

Programs

Mathematica

m = 25; Range[0, m]! * CoefficientList[Series[Exp[-(x + x^2/2 + x^3/3 + x^4/4 + x^5/5)], {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-x^5/5)))

Formula

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