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A286073
Number of permutations of [n] with decreasing cycle sizes.
8
1, 1, 1, 4, 12, 60, 340, 2280, 17220, 151872, 1459584, 15624000, 182318400, 2316837600, 31596570720, 465582237120, 7283287851840, 121620647715840, 2149774858183680, 40196871701360640, 790002144844738560, 16364478334463078400, 354458730544573132800
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
Wikipedia, Permutation
MAPLE
b:= proc(n, i) option remember;
`if`(n>i*(i+1)/2, 0, `if`(n=0, 1, b(n, i-1)+
`if`(i>n, 0, b(n-i, i-1)*(i-1)!*binomial(n-1, i-1))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n > i*(i + 1)/2, 0, If[n == 0, 1, b[n, i - 1] + If[i > n, 0, b[n - i, i - 1]*(i - 1)!*Binomial[n - 1, i - 1]]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 24 2018, translated from Maple *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2017
STATUS
approved