A095987 a(n) = gcd(n!!, (n-1)!!) where n!! = A006882.

1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 45, 45, 315, 315, 315, 315, 2835, 2835, 14175, 14175, 155925, 155925, 467775, 467775, 6081075, 6081075, 42567525, 42567525, 638512875, 638512875, 638512875, 638512875, 10854718875, 10854718875, 97692469875, 97692469875

Offset: 0

Author

Leroy Quet, Jul 18 2004

Keywords

• nonn

Comments

Let f_n(m) be a multifactorial: for m = positive integer, f_n(m) = Product_{k=0..floor((m-1)/n)} (m - k*n). E.g., f_2(m) = m!!. f_n(0) is defined as 1.

Crossrefs

a(2n) gives A049606.

Programs

Maple

a:= n-> (d-> gcd(d(n), d(n-1)))(doublefactorial):
seq(a(n), n=0..40);  # Alois P. Heinz, Oct 26 2019

Mathematica

f[n_] := GCD[n!!, (n - 1)!! ]; Table[ f[n], {n, 35}]
GCD@@#&/@Partition[Range[0,40]!!,2,1] (* Harvey P. Dale, May 04 2015 *)

Formula

a(2m) = a(2m+1) = A049606(m).

Extensions

Edited and extended by Robert G. Wilson v, Jul 19 2004

Missing a(0)=1 inserted by Alois P. Heinz, Oct 26 2019