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A029575 Number of permutations of an n-set containing an 8-cycle. 2

%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 n-set containing an 8-cycle.

%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 1-e^(-1/8).

%F E.g.f.: (1-exp(-x^k/k))/(1-x). - _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_

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Last modified December 2 09:28 EST 2021. Contains 349437 sequences. (Running on oeis4.)