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A364283
Number of permutations of [n] with distinct cycle lengths such that each cycle contains exactly one cycle length different from its own as an element.
3
1, 0, 0, 1, 2, 12, 60, 408, 2640, 24480, 208080, 2262960, 23950080, 307359360, 3835641600, 57400358400, 825160089600, 13909727462400, 229664981145600, 4310966499840000, 79428141112320000, 1658163790483200000, 33795850208440320000, 770528520983789568000
OFFSET
0,5
LINKS
Wikipedia, Permutation
EXAMPLE
a(3) = 1: (13)(2).
a(4) = 2: (124)(3), (142)(3).
a(5) = 12: (1235)(4), (1253)(4), (1325)(4), (1352)(4), (1523)(4), (1532)(4),
(124)(35), (142)(35), (125)(34), (152)(34), (13)(245), (13)(254).
MAPLE
f:= proc(n) option remember; `if`(n<2, 1-n, (n-1)*(f(n-1)+f(n-2))) end:
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!*f(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);
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 17 2023
STATUS
approved