A096471 Number of degree-n permutations with exactly one even cycle.

1, 3, 12, 60, 345, 2415, 18480, 166320, 1596105, 17557155, 202951980, 2638375740, 35703612945, 535554194175, 8307234936000, 141222993912000, 2470641012464625, 46942179236827875, 914462992955011500

Offset: 2

Author

Vladeta Jovovic, Aug 13 2004

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 2..449

Crossrefs

Cf. A060523, A028353.

Programs

Maple

S:= series(-1/2*((1+x)/(1-x))^(1/2)*log(1-x^2), x, 51):
seq(coeff(S,x,n)*n!, n=2..50); # Robert Israel, Nov 13 2017

Formula

E.g.f.: -1/2*((1+x)/(1-x))^(1/2)*log(1-x^2).

Conjecture D-finite with recurrence a(n) -3*a(n-1) +(-2*n^2+8*n-3)*a(n-2) +(n-2)*(4*n-15)*a(n-3) +(n-3)*(n^3-9*n^2+22*n-7)*a(n-4) -(n-3)*(n-4)*(n-5)^2*a(n-5)=0. - R. J. Mathar, Jul 06 2023