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%I #26 Nov 27 2021 20:03:50
%S 1,1,2,12,24,17280,720,87091200,29030400,1755758592000,3628800,
%T 1525930675524002119680000000,479001600,15033074749223731200000,
%U 151533393472175210496000000,2201737050440244933006930739200000000
%N a(n) = Product_{d|n} (n-d)!.
%H G. C. Greubel, <a href="/A135396/b135396.txt">Table of n, a(n) for n = 1..100</a>
%F If p prime, a(p) = (p-1)!. - _Bernard Schott_, Nov 15 2021
%e For n = 6, the divisors of 6 are 1,2,3,6; a(6) = (6-1)! * (6-2)! * (6-3)! * (6-6)! = 17280.
%p 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
%t Table[Product[(n - Divisors[n][[i]])!, {i,1,Length[Divisors[n]]}], {n, 1, 20}] (* _Stefan Steinerberger_, Feb 19 2008 *)
%t Table[Times@@((n-Divisors[n])!),{n,20}] (* _Harvey P. Dale_, Dec 10 2014 *)
%o (PARI) a(n)=my(s=1); fordiv(n,d, s*=(n-d)!); s \\ _Charles R Greathouse IV_, Oct 12 2016
%Y Cf. A000142.
%Y Cf. A000010 (comments on product formulas).
%K easy,nonn
%O 1,3
%A _Ctibor O. Zizka_, Feb 17 2008
%E Definition simplified by _Stefan Steinerberger_, Feb 19 2008
%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Feb 19 2008
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