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A364281
Number of permutations of [n] with distinct cycle lengths such that each cycle contains exactly one cycle length as an element.
5
1, 1, 1, 4, 10, 48, 252, 1584, 10800, 93600, 823680, 8588160, 93381120, 1158312960, 14805504000, 215028172800, 3159494553600, 51973589606400, 873152856576000, 16058241239040000, 300754643245056000, 6159522883497984000, 127439374149255168000
OFFSET
0,4
LINKS
Wikipedia, Permutation
EXAMPLE
a(3) = 4: (123), (132), (13)(2), (1)(23).
a(4) = 10: (1234), (1243), (1324), (1342), (1423), (1432), (124)(3),
(142)(3), (1)(234), (1)(243).
MAPLE
a:= proc(m) option remember; local b; b:=
proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, p!*(m-p)!, b(n, i-1, p)+b(n-i, min(n-i, i-1), p-1)))
end: b(m$3)
end:
seq(a(n), n=0..24);
MATHEMATICA
a[m_] := a[m] = Module[{b}, b[n_, i_, p_] := b[n, i, p] = If[i(i+1)/2 < n, 0, If[n == 0, p!*(m - p)!, b[n, i - 1, p] + b[n - i, Min[n - i, i - 1], p - 1]]]; b[m, m, m]];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Oct 21 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 17 2023
STATUS
approved