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A246195 Number of endofunctions on [n] where the smallest cycle length equals 8. 2
5040, 362880, 18144000, 804988800, 34488115200, 1482082842240, 65120246231040, 2955402450000000, 139296260790086400, 6837541748945107200, 349978565353512775680, 18685433917574232157440, 1040347501174674201600000, 60368458528123335777196800 (list; graph; refs; listen; history; text; internal format)
OFFSET
8,1
LINKS
FORMULA
a(n) ~ (exp(-363/140) - exp(-761/280)) * n^n. - Vaclav Kotesovec, Aug 21 2014
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 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, k), j=0..n):
a:= n-> A(n, 8) -A(n, 9):
seq(a(n), n=8..25);
CROSSREFS
Column k=8 of A246049.
Sequence in context: A179062 A342075 A055362 * A246615 A291114 A246218
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 18 2014
STATUS
approved

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Last modified June 17 11:15 EDT 2024. Contains 373445 sequences. (Running on oeis4.)