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%I #17 Oct 11 2017 20:39:58
%S 0,0,0,0,0,0,120,840,6720,60480,604800,6652800,73180800,951350400,
%T 13318905600,199783584000,3196537344000,54341134848000,
%U 983080530432000,18678530078208000,373570601564160000,7844982632847360000,172589617922641920000,3969561212220764160000
%N Number of permutations of an n-set containing a 6-cycle.
%H Alois P. Heinz, <a href="/A029573/b029573.txt">Table of n, a(n) for n = 0..450</a>
%F a(n) = n! * (1 - sum_{k=0..floor(n/6)} (-1)^k/(k!*6^k)).
%F a(n)/n! is asymptotic to 1-e^(-1/6) = 1 - A092727.
%F E.g.f.: (1-exp(-x^6/6))/(1-x). - _Alois P. Heinz_, Oct 11 2017
%o (PARI) a(n) = n! * (1 - sum(k=0, floor(n/6), (-1)^k/(k!*6^k) ) ); \\ _Michel Marcus_, Aug 08 2013
%Y Column k=6 of A293211.
%K nonn
%O 0,7
%A _Rob Pratt_
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