A110903 Difference between the factorial of n and the double factorial of n.

0, 0, 0, 3, 16, 105, 672, 4935, 39936, 361935, 3624960, 39906405, 478955520, 6226885665, 87177646080, 1307672340975, 20922779566080, 355687393636575, 6402373519933440, 121645099754102925, 2432902004460748800, 51090942157960129425, 1124000727695858073600

Offset: 0

Author

Paolo P. Lava, Sep 21 2005

Keywords

• easy
• nonn

Examples

			a(7) = 7*6*5*4*3*2*1 - 7*5*3*1 = 4935.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000142 (factorials), A006882 (double factorials).

Programs

Mathematica

Table[(n!-n!!), {n,0, 15}] (* Zerinvary Lajos, Mar 21 2007 *)

PARI

a(n)={n! - if(n%2, n!/((n\2)!*2^(n\2)), (n/2)!*2^(n/2))} \\ Andrew Howroyd, Jan 02 2020

Formula

a(n) = n! - n!!.

a(n) = A000142(n) - A006882(n). - Andrew Howroyd, Jan 02 2020

Extensions

Terms a(15) and beyond from Andrew Howroyd, Jan 02 2020