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A291114
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Number of endofunctions on [n] such that the LCM of their cycle lengths equals eight.
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2
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0, 0, 0, 0, 0, 0, 0, 0, 5040, 408240, 22680000, 1105196400, 51492672000, 2386304640720, 112267476921600, 5422473658602000, 270574193944454400, 13996921541118516000, 752006571801610245120, 41994571006059763946400, 2437848824911611890688000
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OFFSET
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0,9
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..387
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FORMULA
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a(n) ~ (4*exp(15/8) - 3*exp(7/4)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017
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MAPLE
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b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
`if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
*binomial(n-1, j-1)*(j-1)!, j=1..n))))(8)
end:
a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..22);
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CROSSREFS
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Column k=8 of A222029.
Sequence in context: A055362 A246195 A246615 * A246218 A178140 A180369
Adjacent sequences: A291111 A291112 A291113 * A291115 A291116 A291117
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Aug 17 2017
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STATUS
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approved
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