A029575 - OEIS

A029575

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

0, 0, 0, 0, 0, 0, 0, 0, 5040, 45360, 453600, 4989600, 59875200, 778377600, 10897286400, 163459296000, 2451889440000, 41682120480000, 750278168640000, 14255285204160000, 285105704083200000, 5987219785747200000, 131718835286438400000, 3029533211588083200000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,9

LINKS

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

FORMULA

a(n) = n! * (1 - Sum_{k=0..floor(n/8)} (-1)^k/(k!*8^k) ).

a(n)/n! is asymptotic to 1-e^(-1/8).

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

PROG

(PARI) a(n) = n! * (1 - sum(k=0, floor(n/8), (-1)^k/(k!*8^k) ) ); \\ Michel Marcus, Aug 08 2013

CROSSREFS