login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286071 Number of permutations of [n] with nonincreasing cycle sizes. 8
1, 1, 2, 5, 19, 85, 496, 3229, 25117, 215225, 2100430, 22187281, 261228199, 3284651245, 45163266604, 659277401525, 10380194835601, 172251467909809, 3057368096689690, 56867779157145769, 1122474190194034555, 23137433884903034501, 502874858021076645784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.

a(n) is even if and only if n in { A016825 }.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

Wikipedia, Permutation

EXAMPLE

a(3) = 5: (123), (132), (12)(3), (13)(2), (1)(2)(3).

a(4) = 19: (1234), (1243), (1324), (1342), (1423), (1432), (123)(4), (132)(4), (124)(3), (142)(3), (12)(34), (12)(3)(4), (134)(2), (143)(2), (13)(24), (13)(2)(4), (14)(23), (14)(2)(3), (1)(2)(3)(4).

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, add((j-1)!*

      b(n-j, j)*binomial(n-1, j-1), j=1..min(n, i)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[(j - 1)!*b[n - j, j]*Binomial[n - 1, j - 1], {j, 1, Min[n, i]}]];

a[n_] := b[n, n];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 24 2018, translated from Maple *)

CROSSREFS

Cf. A016825, A275310, A286072, A286073, A286074, A286075, A286076, A286077.

Sequence in context: A107377 A286886 A058132 * A002851 A324618 A326563

Adjacent sequences:  A286068 A286069 A286070 * A286072 A286073 A286074

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)