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A246217
Number of endofunctions on [n] where the largest cycle length equals 7.
2
720, 46080, 2099520, 86400000, 3478701600, 141893959680, 5963619055680, 260480095349760, 11874161338182000, 565994948205772800, 28225084763940704640, 1472185000741804277760, 80257688278285346487360, 4568639693232433397760000, 271256500003796168962953600
OFFSET
7,1
LINKS
FORMULA
a(n) ~ (7*exp(363/140) - 6*exp(49/20)) * 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, 7) -A(n, 6):
seq(a(n), n=7..25);
CROSSREFS
Column k=7 of A241981.
Sequence in context: A246194 A246614 A291113 * A364771 A003931 A158049
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 19 2014
STATUS
approved