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

0,4

Links

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

Formula

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A368934 A344216 A105622 * A206351 A085614 A215931

Adjacent sequences: A110900 A110901 A110902 * A110904 A110905 A110906

Keyword

easy,nonn

Author

Paolo P. Lava, Sep 21 2005

Extensions

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

Status

approved