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 A029575 #16 Oct 11 2017 20:47:08 %S A029575 0,0,0,0,0,0,0,0,5040,45360,453600,4989600,59875200,778377600, %T A029575 10897286400,163459296000,2451889440000,41682120480000, %U A029575 750278168640000,14255285204160000,285105704083200000,5987219785747200000,131718835286438400000,3029533211588083200000 %N A029575 Number of permutations of an n-set containing an 8-cycle. %H A029575 Alois P. Heinz, <a href="/A029575/b029575.txt">Table of n, a(n) for n = 0..450</a> %F A029575 a(n) = n! * (1 - Sum_{k=0..floor(n/8)} (-1)^k/(k!*8^k) ). %F A029575 a(n)/n! is asymptotic to 1-e^(-1/8). %F A029575 E.g.f.: (1-exp(-x^k/k))/(1-x). - _Alois P. Heinz_, Oct 11 2017 %o A029575 (PARI) a(n) = n! * (1 - sum(k=0, floor(n/8), (-1)^k/(k!*8^k) ) ); \\ _Michel Marcus_, Aug 08 2013 %Y A029575 Column k=8 of A293211. %K A029575 nonn %O A029575 0,9 %A A029575 _Rob Pratt_