A070734 Order of the subgroup of the symmetric group S_n generated by the cycles (1,2,3) and (1,2,3,...,n).
3, 24, 60, 720, 2520, 40320, 181440, 3628800, 19958400, 479001600, 3113510400, 87178291200, 653837184000, 20922789888000, 177843714048000, 6402373705728000, 60822550204416000, 2432902008176640000
Offset: 3
Programs
-
Mathematica
f[n_] := If[ EvenQ[n], n!, n!/2]; Table[ f[n], {n, 3, 24}] -
PARI
for(n=3,20,print1((3+(-1)^n)/4*n!,","))
Formula
For odd n: a(n) = n!/2; for even n: a(n) = n!.
a(n) = (1/4)*(3+(-1)^n)*n! - Benoit Cloitre, May 18 2002
From Amiram Eldar, Jul 06 2022: (Start)
Sum_{n>=3} 1/a(n) = 2*sinh(1) + cosh(1) - 7/2.
Sum_{n>=3} (-1)^(n+1)/a(n) = 2*sinh(1) - cosh(1) - 1/2. (End)
Extensions
More terms from Benoit Cloitre, May 18 2002