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A212291 Number of permutations of n elements with at most one fixed point. 2
1, 1, 1, 5, 17, 89, 529, 3709, 29665, 266993, 2669921, 29369141, 352429681, 4581585865, 64142202097, 962133031469, 15394128503489, 261700184559329, 4710603322067905, 89501463119290213, 1790029262385804241, 37590614510101889081, 826993519222241559761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Agrees with the number of maximal matchings in the n-crown graph up to at least n = 10. - Eric W. Weisstein, Jun 14-Dec 30 2017

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

Eric Weisstein's World of Mathematics, Crown Graph

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Maximal Independent Edge Set

FORMULA

a(n) = 2/e * n! + O(n).

a(n) = 2*!n - (-1)^n, where !n is the subfactorial. - Eric W. Weisstein, Dec 30 2017

a(n) = A000166(n) + A000240(n).

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

MAPLE

b:= proc(n) b(n):= `if` (n<1, 1, n*b(n-1)+(-1)^(n)) end:

a:= n-> b(n) +n*b(n-1):

seq(a(n), n=0..30);  # Alois P. Heinz, Jun 17 2012

MATHEMATICA

nn=20; Range[0, nn]!CoefficientList[Series[(1+x)Exp[-x]/(1-x), {x, 0, nn}], x] (* Geoffrey Critzer, Sep 27 2013 *)

Table[(-1)^n (HypergeometricPFQ[{1, -n}, {}, 1] - n HypergeometricPFQ[{1, 1 - n}, {}, 1]), {n, 20}] (* Eric W. Weisstein, Jun 14 2017 *)

Table[2 Subfactorial[n] - (-1)^n, {n, 20}] (* Eric W. Weisstein, Dec 30 2017 *)

PROG

(PARI) d(n)=if(n, round(n!/exp(1)), 1)

a(n)=if(n, n*d(n-1))+d(n)

CROSSREFS

Cf. A000166, A000240.

Sequence in context: A026685 A089923 A145041 * A307176 A179684 A250744

Adjacent sequences:  A212288 A212289 A212290 * A212292 A212293 A212294

KEYWORD

nonn,easy

AUTHOR

Charles R Greathouse IV, Jun 17 2012

STATUS

approved

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)