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A246195 Number of endofunctions on [n] where the smallest cycle length equals 8. 2

%I #6 Aug 21 2014 05:32:35

%S 5040,362880,18144000,804988800,34488115200,1482082842240,

%T 65120246231040,2955402450000000,139296260790086400,

%U 6837541748945107200,349978565353512775680,18685433917574232157440,1040347501174674201600000,60368458528123335777196800

%N Number of endofunctions on [n] where the smallest cycle length equals 8.

%H Alois P. Heinz, <a href="/A246195/b246195.txt">Table of n, a(n) for n = 8..200</a>

%F a(n) ~ (exp(-363/140) - exp(-761/280)) * n^n. - _Vaclav Kotesovec_, Aug 21 2014

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,

%p add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

%p b(n-i*j, i+1), j=0..n/i)))

%p end:

%p A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):

%p a:= n-> A(n, 8) -A(n, 9):

%p seq(a(n), n=8..25);

%Y Column k=8 of A246049.

%K nonn

%O 8,1

%A _Alois P. Heinz_, Aug 18 2014

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Last modified July 13 18:54 EDT 2024. Contains 374285 sequences. (Running on oeis4.)