login
A246197
Number of endofunctions on [n] where the smallest cycle length equals 10.
2
362880, 39916800, 2874009600, 175394419200, 9967384627200, 551675124000000, 30471021291110400, 1703458301210265600, 97213825272736972800, 5693251850259515942400, 343266609438110040883200, 21349182724237331665228800, 1371132989012608561874534400
OFFSET
10,1
COMMENTS
In general, number of endofunctions on [n] where the smallest cycle length equals k is asymptotic to (exp(-H(k-1)) - exp(-H(k))) * n^n, where H(k) is the harmonic number A001008/A002805, k>=1. - Vaclav Kotesovec, Aug 21 2014
LINKS
FORMULA
a(n) ~ (exp(-7129/2520) - exp(-7381/2520))* 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, 10) -A(n, 11):
seq(a(n), n=10..25);
CROSSREFS
Column k=10 of A246049.
Sequence in context: A228912 A213871 A179064 * A246617 A246220 A160319
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 18 2014
STATUS
approved