A005096 a(n) = n! - n.

1, 0, 0, 3, 20, 115, 714, 5033, 40312, 362871, 3628790, 39916789, 479001588, 6227020787, 87178291186, 1307674367985, 20922789887984, 355687428095983, 6402373705727982, 121645100408831981, 2432902008176639980, 51090942171709439979, 1124000727777607679978

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

McCombinations: in 2002, McDonald's advertised a McChoice menu of 8 items under the heading "40,312 combinations" rather than the more obvious 2^8-1=255 (A000225). The Advertising Standards Authority "considered that the number quoted in the advertisement was not necessarily so exaggerated as to be misleading". - Henry Bottomley, May 01 2003

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Advertising Standards Authority, McDonald's Restaurants Ltd (archived May 10 2004).
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142, A033312.

Programs

Magma

[Factorial(n) - n: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011

Maple

A005096:=n->n!-n: seq(A005096(n), n=0..25); # Wesley Ivan Hurt, Oct 28 2014

Mathematica

lst={};Do[AppendTo[lst, n!-n], {n, 3*4!}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 20 2008 *)
Table[n! - n, {n, 0, 25}] (* Wesley Ivan Hurt, Oct 28 2014 *)

PARI

a(n)=n!-n \\ Charles R Greathouse IV, Oct 28 2014

Formula

a(n) = n*a(n-1)+n(n-2) = n*A033312(n-1) = A000142(n)-n. - Henry Bottomley, May 01 2003

E.g.f.: 1/(1 - x) - x*exp(x). - Ilya Gutkovskiy, Jan 27 2017