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A145219 a(n) is the number of even permutations (of an n-set) with exactly 1 fixed point. 3
1, 0, 0, 8, 15, 144, 910, 7440, 66717, 667520, 7342236, 88107480, 1145396395, 16035550608, 240533257770, 3848532125984, 65425046139705, 1177650830517120, 22375365779822392, 447507315596451240, 9397653627525472071, 206748379805560390160, 4755212735527888968390 (list; graph; refs; listen; history; text; internal format)
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).

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

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)