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A029572 Number of permutations of an n-set containing a 5-cycle. 2
0, 0, 0, 0, 0, 24, 144, 1008, 8064, 72576, 653184, 7185024, 86220288, 1120863744, 15692092416, 237124952064, 3793999233024, 64497986961408, 1160963765305344, 22058311540801536, 441004037348818944, 9261084784325197824, 203743865255154352128, 4686108900868550098944 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(n) = n! (1 - sum(k=0...floor(n/5), (-1)^k/(k!*5^k)).

a(n)/n! is asymptotic to 1-e^(-1/5) = 1 - A092618.

E.g.f.: (1-exp(-x^5/5))/(1-x) - Geoffrey Critzer, Jun 01 2013

MATHEMATICA

nn = 20; a = Log[1/(1 - x)] - x^5/5;

Range[0, nn]! CoefficientList[Series[1/(1 - x) - Exp[a], {x, 0, nn}], x]

(* Geoffrey Critzer, Jun 01 2013 *)

PROG

(PARI) x='x+O('x^66); concat([0, 0, 0, 0, 0], Vec(serlaplace((1-exp(-x^5/5))/(1-x)))) \\ Joerg Arndt, Jun 01 2013

CROSSREFS

Column k=5 of A293211.

Sequence in context: A054118 A223373 A001342 * A129923 A064138 A158047

Adjacent sequences:  A029569 A029570 A029571 * A029573 A029574 A029575

KEYWORD

nonn

AUTHOR

Rob Pratt

STATUS

approved

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)