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A291113
Number of endofunctions on [n] such that the LCM of their cycle lengths equals seven.
2
0, 0, 0, 0, 0, 0, 0, 720, 46080, 2073600, 83635200, 3284582400, 130292997120, 5315938467840, 225174409574400, 9949921392153600, 459690572096870400, 22223242784959856640, 1124142765926532618240, 59464928954695680000000, 3286601083552719895603200
OFFSET
0,8
LINKS
FORMULA
a(n) ~ (2*exp(8/7)-exp(1)) * 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))))(7)
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=7 of A222029.
Sequence in context: A092716 A246194 A246614 * A246217 A364771 A003931
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 17 2017
STATUS
approved