A145219 a(n) is the number of even permutations (of an n-set) with exactly 1 fixed point.

1, 0, 0, 8, 15, 144, 910, 7440, 66717, 667520, 7342236, 88107480, 1145396395, 16035550608, 240533257770, 3848532125984, 65425046139705, 1177650830517120, 22375365779822392, 447507315596451240, 9397653627525472071, 206748379805560390160, 4755212735527888968390

Offset: 1

Author

Abdullahi Umar, Oct 09 2008

Keywords

• nonn

Examples

			a(4) = 8 because there are exactly 8 even permutations (of a 4-set) having 1 fixed point, namely: (123), (132), (124), (142), (134), (143), (234), (243).
		

Links

• Bashir Ali and A. Umar, Some combinatorial properties of the alternating group, Southeast Asian Bulletin Math. 32 (2008), 823-830.

Crossrefs

Cf. A003221, A145220, A145222.

Programs

PARI

x = 'x + O('x^30); Vec(serlaplace((x*(1-x^2/2) * exp(-x))/(1-x))) \\ Michel Marcus, Apr 04 2016

Formula

a(n) = n*A003221(n-1), (n > 0).

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

D-finite with recurrence (-3*n+7)*a(n) +(n-2)*(3*n-10)*a(n-1) +(9*n-8)*(n-3)*a(n-2) +2*(3*n-2)*(n-2)*a(n-3)=0. - R. J. Mathar, Jul 06 2023

Extensions

More terms from Alois P. Heinz, Nov 19 2013