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 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-François 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

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