A135396 a(n) = Product_{d|n} (n-d)!.

1, 1, 2, 12, 24, 17280, 720, 87091200, 29030400, 1755758592000, 3628800, 1525930675524002119680000000, 479001600, 15033074749223731200000, 151533393472175210496000000, 2201737050440244933006930739200000000

Offset: 1

Author

Ctibor O. Zizka, Feb 17 2008

Keywords

• easy
• nonn

Examples

			For n = 6, the divisors of 6 are 1,2,3,6; a(6) = (6-1)! * (6-2)! * (6-3)! * (6-6)! = 17280.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000142.

Cf. A000010 (comments on product formulas).

Programs

Maple

A135396 := proc(n) local dvs ; dvs := numtheory[divisors](n) minus {n} ; mul( (n-i)!,i=dvs) ; end: seq(A135396(n),n=1..30) ; # R. J. Mathar, Feb 19 2008

Mathematica

Table[Product[(n - Divisors[n][[i]])!, {i,1,Length[Divisors[n]]}], {n, 1, 20}] (* Stefan Steinerberger, Feb 19 2008 *)
Table[Times@@((n-Divisors[n])!),{n,20}] (* Harvey P. Dale, Dec 10 2014 *)

PARI

a(n)=my(s=1); fordiv(n,d, s*=(n-d)!); s \\ Charles R Greathouse IV, Oct 12 2016

Formula

If p prime, a(p) = (p-1)!. - Bernard Schott, Nov 15 2021

Extensions

Definition simplified by Stefan Steinerberger, Feb 19 2008

More terms from R. J. Mathar and Stefan Steinerberger, Feb 19 2008