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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000142.

Cf. A000010 (comments on product formulas).

Sequence in context: A091137 A347284 A092825 * A031048 A294554 A098707

Adjacent sequences: A135393 A135394 A135395 * A135397 A135398 A135399

Keyword

easy,nonn

Author

Ctibor O. Zizka, Feb 17 2008

Extensions

Definition simplified by Stefan Steinerberger, Feb 19 2008

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

Status

approved