A069660 Order of the subgroup of the symmetric group S_n generated by the cycles (1,3) and (1,2,3,...,n).

6, 8, 120, 72, 5040, 1152, 362880, 28800, 39916800, 1036800, 6227020800, 50803200, 1307674368000, 3251404800, 355687428096000, 263363788800, 121645100408832000, 26336378880000, 51090942171709440000, 3186701844480000, 25852016738884976640000, 458885065605120000

Offset: 3

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 16 2002

Keywords

• nonn
• easy

Crossrefs

Cf. A000984, A070734, A000142, A009445, A001044.

Programs

Mathematica

a[n_] := If[OddQ[n], n!, 2 * ((n/2)!)^2]; Array[a, 20, 3] (* Amiram Eldar, Jul 12 2025 *)

PARI

a(n) = if(n % 2, n!, 2 * ((n/2)!)^2); \\ Amiram Eldar, Jul 12 2025

Formula

If n is odd a(n) = n!, if n is even a(n) = 2 * ((n/2)!)^2 = 2 * n! / A000984(n/2) = 2 * A001044(n/2).

Sum_{n>=3} 1/a(n) = BesselI(0, 2)/2 + sinh(1) - 2. - Amiram Eldar, Jul 12 2025

Extensions

More terms from Benoit Cloitre, May 20 2002