A166554 a(0)=1, a(n) = n*(a(n-1) - 1) for n>0.

1, 0, -2, -9, -40, -205, -1236, -8659, -69280, -623529, -6235300, -68588311, -823059744, -10699776685, -149796873604, -2246953104075, -35951249665216, -611171244308689, -11001082397556420, -209020565553571999

Offset: 0

Author

Philippe Deléham, Oct 16 2009

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000142, A038156, A165793, A165814.

Programs

Magma

[n le 1 select 1 else (n-1)*(Self(n-1) - 1): n in [1..41]]; // G. C. Greubel, Nov 30 2024

Mathematica

RecurrenceTable[{a[0]==1,a[n]==n(a[n-1]-1)},a[n],{n,20}] (* Harvey P. Dale, Jul 25 2011 *)

Python

def A166554(n): return 1 +factorial(n) -int(exp(1)*factorial(n)) +int(n==0)
print([A166554(n) for n in range(41)]) # G. C. Greubel, Nov 30 2024

Formula

a(n) = -A038156(n) for n>0.

a(n) = n! - floor(e*n!) + 1, n>0. - Gary Detlefs, Jun 06 2010

a(n) = (n+2)*a(n-1) - (2*n-1)*a(n-2) + (n-2)*a(n-3). - R. J. Mathar, Jul 28 2013