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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2017
STATUS
approved