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 A286075 Number of permutations of [n] with increasing cycle sizes. 8
 1, 1, 1, 3, 8, 38, 182, 1194, 7932, 69192, 591936, 6286272, 66914880, 840036960, 10567285920, 154755036000, 2246755924800, 37283584936320, 618705247829760, 11472473012232960, 212762383625594880, 4386435706887413760, 89954629722500659200, 2030764767987849062400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..450 Wikipedia, Permutation MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0, b(n, i+1)+b(n-i, i+1)*(i-1)!*binomial(n-1, i-1))) end: a:= n-> b(n, 1): seq(a(n), n=0..30); MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i + 1] + b[n - i, i + 1]*(i - 1)!*Binomial[n - 1, i - 1]]]; a[n_] := b[n, 1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 28 2018, from Maple *) CROSSREFS Cf. A275312, A286071, A286072, A286073, A286074, A286076, A286077. Sequence in context: A123981 A123985 A219953 * A089066 A099030 A264657 Adjacent sequences: A286072 A286073 A286074 * A286076 A286077 A286078 KEYWORD nonn AUTHOR Alois P. Heinz, May 01 2017 STATUS approved

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Last modified December 2 23:17 EST 2023. Contains 367526 sequences. (Running on oeis4.)