This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A029574 #16 Oct 11 2017 20:43:16 %S A029574 0,0,0,0,0,0,0,720,5760,51840,518400,5702400,68428800,889574400, %T A029574 11564467200,173467008000,2775472128000,47183026176000, %U A029574 849294471168000,16136594952192000,322731899043840000,6802195410616320000,149648299033559040000,3441910877771857920000 %N A029574 Number of permutations of an n-set containing a 7-cycle. %H A029574 Alois P. Heinz, <a href="/A029574/b029574.txt">Table of n, a(n) for n = 0..450</a> %F A029574 a(n) = n! * (1 - sum_{k=0..floor(n/7)} (-1)^k/(k!*7^k)). %F A029574 a(n)/n! is asymptotic to 1-e^(-1/7) = 1 - A092750. %F A029574 E.g.f.: (1-exp(-x^7/7))/(1-x). - _Alois P. Heinz_, Oct 11 2017 %o A029574 (PARI) a(n) = n! * (1 - sum(k=0, floor(n/7), (-1)^k/(k!*7^k) ) ); \\ _Michel Marcus_, Aug 08 2013 %Y A029574 Column k=7 of A293211. %K A029574 nonn %O A029574 0,8 %A A029574 _Rob Pratt_