A029574 Number of permutations of an n-set containing a 7-cycle.

0, 0, 0, 0, 0, 0, 0, 720, 5760, 51840, 518400, 5702400, 68428800, 889574400, 11564467200, 173467008000, 2775472128000, 47183026176000, 849294471168000, 16136594952192000, 322731899043840000, 6802195410616320000, 149648299033559040000, 3441910877771857920000

Offset: 0

Author

Rob Pratt

Keywords

• nonn

Links

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

Crossrefs

Column k=7 of A293211.

Programs

PARI

a(n) = n! * (1 - sum(k=0, floor(n/7), (-1)^k/(k!*7^k) ) ); \\ Michel Marcus, Aug 08 2013

Formula

a(n) = n! * (1 - sum_{k=0..floor(n/7)} (-1)^k/(k!*7^k)).

a(n)/n! is asymptotic to 1-e^(-1/7) = 1 - A092750.

E.g.f.: (1-exp(-x^7/7))/(1-x). - Alois P. Heinz, Oct 11 2017