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

2,2

Links

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

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

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

Crossrefs

Cf. A060523, A028353.

Sequence in context: A092803 A181282 A020052 * A140097 A105227 A370652

Adjacent sequences: A096468 A096469 A096470 * A096472 A096473 A096474

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 13 2004

Status

approved