%I
%S 0,0,0,0,0,0,0,0,5040,45360,453600,4989600,59875200,778377600,
%T 10897286400,163459296000,2451889440000,41682120480000,
%U 750278168640000,14255285204160000,285105704083200000,5987219785747200000,131718835286438400000,3029533211588083200000
%N Number of permutations of an nset containing an 8cycle.
%H Alois P. Heinz, <a href="/A029575/b029575.txt">Table of n, a(n) for n = 0..450</a>
%F a(n) = n! * (1  Sum_{k=0..floor(n/8)} (1)^k/(k!*8^k) ).
%F a(n)/n! is asymptotic to 1e^(1/8).
%F E.g.f.: (1exp(x^k/k))/(1x).  _Alois P. Heinz_, Oct 11 2017
%o (PARI) a(n) = n! * (1  sum(k=0, floor(n/8), (1)^k/(k!*8^k) ) ); \\ _Michel Marcus_, Aug 08 2013
%Y Column k=8 of A293211.
%K nonn
%O 0,9
%A _Rob Pratt_
