A070740 Order of the subgroup of the symmetric group S_(2n) generated by the 2 cycles: (1,2,...n,2n,2n-1,...,n+1) and (1,2,...,2n).

24, 36, 40320, 7200, 479001600, 25401600, 20922789888000, 65840947200, 2432902008176640000, 1593350922240000, 620448401733239439360000, 19387894021816320000, 304888344611713860501504000000, 1710012252724199424000000, 263130836933693530167218012160000000

Offset

2,1

Links

Andrew Howroyd, Table of n, a(n) for n = 2..100

Formula

If n is even: a(n) = (2n)!.

If n is congruent to 1 mod 4: a(n) = (n!)^2 / 2.

If n is congruent to 3 mod 4: a(n) = (n!)^2.

Mathematica

a[n_] := Switch[Mod[n, 4], 0, (2*n)!, 1, (n!)^2 / 2, 2, (2*n)!, 3, (n!)^2]; Array[a, 20, 2] (* Amiram Eldar, Jul 12 2025 *)

Prog

(PARI) a(n) = if(n < 2, 0, if(n%2==0, (2*n)!, (n!)^2 / if(n%4==1, 2, 1))); \\ Andrew Howroyd, Jul 04 2018

Crossrefs

Cf. A001044, A010050.

Sequence in context: A241286 A380568 A334803 * A175460 A015805 A164534

Adjacent sequences: A070737 A070738 A070739 * A070741 A070742 A070743

Keyword

nonn

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 14 2002

Extensions

Terms a(8) and beyond from Andrew Howroyd, Jul 04 2018

Status

approved