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A246218 Number of endofunctions on [n] where the largest cycle length equals 8. 2
5040, 408240, 22680000, 1106859600, 51732172800, 2408384618640, 113960430904320, 5541379593750000, 278592031202284800, 14529619059476320800, 787422201081850414080, 44373594768472437642720, 2600326096882824360960000, 158404803877320370312773600 (list; graph; refs; listen; history; text; internal format)
OFFSET
8,1
LINKS
FORMULA
a(n) ~ (8*exp(761/280) - 7*exp(363/140)) * n^(n-1). - Vaclav Kotesovec, Aug 21 2014
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i-1), j=0..n/i)))
end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
a:= n-> A(n, 8) -A(n, 7):
seq(a(n), n=8..25);
CROSSREFS
Column k=8 of A241981.
Sequence in context: A246195 A246615 A291114 * A178140 A180369 A053876
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 19 2014
STATUS
approved

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Last modified July 18 17:38 EDT 2024. Contains 374388 sequences. (Running on oeis4.)