A092238 Number of ways to write the permutation n,n-1,...,1 of 1,2,...,n as a product of n(n-1)/2 transpositions, where each transposition of 1,2,...,n occurs exactly once.

1, 1, 1, 2, 64, 59712, 3580519776

Offset: 0

Author

Richard Stanley, Feb 19 2004

Keywords

• more
• nonn

Comments

If we impose the additional condition on the product t_1 t_2 ... of transpositions that the number of inversions increases by one each time we multiply by a t_i, then the number of ways is given by A005118.

Examples

			a(3)=2 because 321 = (1,2)(1,3)(2,3) = (2,3)(1,3)(1,2).
		

Crossrefs

Cf. A005118.

Extensions

a(0)=1 prepended and a(6) added by Alois P. Heinz, Jul 12 2017