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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 02 2009
STATUS
approved