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A291112
Number of endofunctions on [n] such that the LCM of their cycle lengths equals six.
2
0, 0, 0, 0, 0, 20, 840, 26250, 773920, 23166360, 724253040, 23921630810, 838352908800, 31203417745500, 1232550480801640, 51590674307982810, 2283883442833836480, 106713738151299297200, 5251783507905871571040, 271673904611812139017650, 14743195769771119241426080
OFFSET
0,6
LINKS
FORMULA
a(n) ~ (exp(1) - 2*exp(4/3) - 2*exp(3/2) + 4*exp(2)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017
MAPLE
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))))(6)
end:
a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..22);
CROSSREFS
Column k=6 of A222029.
Sequence in context: A292417 A117798 A006424 * A362168 A192370 A113102
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 17 2017
STATUS
approved