A029573 - OEIS

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A029573

Number of permutations of an n-set containing a 6-cycle.

0, 0, 0, 0, 0, 0, 120, 840, 6720, 60480, 604800, 6652800, 73180800, 951350400, 13318905600, 199783584000, 3196537344000, 54341134848000, 983080530432000, 18678530078208000, 373570601564160000, 7844982632847360000, 172589617922641920000, 3969561212220764160000

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OFFSET

0,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) = n! * (1 - sum_{k=0..floor(n/6)} (-1)^k/(k!*6^k)).

a(n)/n! is asymptotic to 1-e^(-1/6) = 1 - A092727.

E.g.f.: (1-exp(-x^6/6))/(1-x). - Alois P. Heinz, Oct 11 2017

PROG

(PARI) a(n) = n! * (1 - sum(k=0, floor(n/6), (-1)^k/(k!*6^k) ) ); \\ Michel Marcus, Aug 08 2013

CROSSREFS