A161122 Number of cycles with entries of the same parity in all fixed-point-free involutions of {1,2,...,2n}.

0, 0, 2, 18, 180, 2100, 28350, 436590, 7567560, 145945800, 3101348250, 72020198250, 1814908995900, 49332526343100, 1438865351673750, 44826189802143750, 1485668004871050000, 52196469237802890000, 1937793920453432291250, 75801938653031321981250, 3116301922402398792562500

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = n(n-1)(2n-3)!!.

a(n) = Sum_{k>=0} k*A161121(n,k).

D-finite with recurrence (-n+2)*a(n) +n*(2*n-3)*a(n-1)=0. - R. J. Mathar, Jul 26 2022

Example

a(2)=2 because in the 3 permutations (12)(34), (13)(24), (14)(23) we have a total of 2 cycles with entries of the same parity.

Maple

seq(n*(n-1)*(product(2*j-1, j = 1 .. n-1)), n = 0 .. 18);

Mathematica

Table[n (n - 1) (2 n -3)!!, {n, 0, 20}] (* Vincenzo Librandi, Jul 21 2017 *)

Prog

(Magma) DoubleFactorial:=func< n | &*[n..2 by -2] >; [ n*(n-1)*DoubleFactorial(2*n-3): n in [0..22]]; // Vincenzo Librandi, Jul 21 2017

Crossrefs

Cf. A161119, A161120, A161121.

Sequence in context: A214768 A337855 A099044 * A019581 A183285 A359458

Adjacent sequences: A161119 A161120 A161121 * A161123 A161124 A161125

Keyword

nonn

Author

Emeric Deutsch, Jun 02 2009

Status

approved