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

1,4

Links

Table of n, a(n) for n=1..23.

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

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

Example

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).

Prog

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

Crossrefs

Cf. A003221, A145220, A145222.

Sequence in context: A234534 A067686 A283821 * A002406 A212593 A153700

Adjacent sequences: A145216 A145217 A145218 * A145220 A145221 A145222

Keyword

nonn

Author

Abdullahi Umar, Oct 09 2008

Extensions

More terms from Alois P. Heinz, Nov 19 2013

Status

approved