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A215916 The total number of components (cycles) in all alignments. 3
0, 1, 5, 32, 254, 2414, 26746, 338568, 4820952, 76270032, 1327263024, 25196689968, 518190651744, 11476753967184, 272339818023984, 6893370154797312, 185387657162396544, 5279022594143270784, 158674547929990485888, 5020389181983702415104, 166784921186052433648896 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

An alignment is a sequence of cycles of an n-permutation, cf. A007840.

LINKS

Table of n, a(n) for n=0..20.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 180.

FORMULA

a(n) = Sum_{k=1...n} s(n,k)*k!*k where s(n,k) is the unsigned Stirling number of the first kind (A132393).

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

a(n) ~ n!*n*exp(n)/(exp(1)-1)^(n+2) . - Vaclav Kotesovec, Sep 24 2013

MATHEMATICA

nn = 20; a = Log[1/(1 - x)]; Range[0, nn]! CoefficientList[

  D[Series[1/(1 - y a), {x, 0, nn}], y] /. y -> 1, x]

CROSSREFS

Cf. A007840, A132393.

Sequence in context: A241769 A208046 A198598 * A068102 A166993 A328055

Adjacent sequences:  A215913 A215914 A215915 * A215917 A215918 A215919

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Aug 27 2012

STATUS

approved

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Last modified July 12 11:25 EDT 2020. Contains 335658 sequences. (Running on oeis4.)