A215916 The total number of components (cycles) in all alignments.

0, 1, 5, 32, 254, 2414, 26746, 338568, 4820952, 76270032, 1327263024, 25196689968, 518190651744, 11476753967184, 272339818023984, 6893370154797312, 185387657162396544, 5279022594143270784, 158674547929990485888, 5020389181983702415104, 166784921186052433648896

Offset

0,3

Comments

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

Links

Seiichi Manyama, Table of n, a(n) for n = 0..417

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

E.g.f.: Sum_{k>=0} k * (-log(1-x))^k. - Seiichi Manyama, Apr 22 2022

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]

Prog

(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, N, k*(-log(1-x))^k)))) \\ Seiichi Manyama, Apr 22 2022

Crossrefs

Cf. A007840, A132393.

Sequence in context: A208046 A198598 A369785 * A068102 A166993 A328055

Adjacent sequences: A215913 A215914 A215915 * A215917 A215918 A215919

Keyword

nonn

Author

Geoffrey Critzer, Aug 27 2012

Status

approved