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A135396
a(n) = Product_{d|n} (n-d)!.
2
1, 1, 2, 12, 24, 17280, 720, 87091200, 29030400, 1755758592000, 3628800, 1525930675524002119680000000, 479001600, 15033074749223731200000, 151533393472175210496000000, 2201737050440244933006930739200000000
OFFSET
1,3
LINKS
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
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