%I #17 Dec 13 2019 05:40:15
%S 0,0,0,0,0,0,0,0,0,0,362880,3991680,47900160,622702080,8717829120,
%T 130767436800,2092278988800,35568742809600,640237370572800,
%U 12164510040883200,231125690776780800,4853639506312396800,106780069138872729600,2455941590194072780800
%N Number of permutations of an n-set containing a 10-cycle.
%H Alois P. Heinz, <a href="/A029577/b029577.txt">Table of n, a(n) for n = 0..450</a>
%F a(n) = n! * (1 - Sum_{k=0..floor(n/10)} (-1)^k/(k!10^k));
%F a(n)/n! is asymptotic to 1-e^(-1/10).
%F E.g.f.: (1-exp(-x^10/10))/(1-x). - _Alois P. Heinz_, Oct 11 2017
%F Conjectures from _Stéphane Rézel_, Dec 11 2019: (Start)
%F Recurrence: a(n) = n*a(n-1), for n > 10 and n !== 0 (mod 10);
%F for k > 1, a(10*k) = a(10*k-1)*S(k)/S(k-1) where S(k) = 10*k*S(k-1) - (-1)^k with S(1) = 1.
%F (End)
%o (PARI) a(n) = n! * (1 - sum(k=0, floor(n/10), (-1)^k/(k!*10^k) ) ); \\ _Stéphane Rézel_, Dec 11 2019
%Y Column k=10 of A293211.
%K nonn
%O 0,11
%A _Rob Pratt_