cp's OEIS Frontend

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.

A029575 Number of permutations of an n-set containing an 8-cycle.

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%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_