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 A029572 #26 Aug 06 2024 09:56:18
%S A029572 0,0,0,0,0,24,144,1008,8064,72576,653184,7185024,86220288,1120863744,
%T A029572 15692092416,237124952064,3793999233024,64497986961408,
%U A029572 1160963765305344,22058311540801536,441004037348818944,9261084784325197824,203743865255154352128,4686108900868550098944
%N A029572 Number of permutations of an n-set containing a 5-cycle.
%F A029572 a(n) = n!*(1 - Sum_{k=0..floor(n/5)} (-1)^k/(k!*5^k)).
%F A029572 a(n)/n! is asymptotic to 1-e^(-1/5) = 1 - A092618.
%F A029572 E.g.f.: (1-exp(-x^5/5))/(1-x) - _Geoffrey Critzer_, Jun 01 2013
%t A029572 nn = 20; a = Log[1/(1 - x)] - x^5/5; Range[0, nn]! CoefficientList[Series[1/(1 - x) - Exp[a], {x, 0, nn}],x] (* _Geoffrey Critzer_, Jun 01 2013 *)
%o A029572 (PARI) my(x='x+O('x^66)); concat([0,0,0,0,0], Vec(serlaplace((1-exp(-x^5/5))/(1-x)))) \\ _Joerg Arndt_, Jun 01 2013
%Y A029572 Column k=5 of A293211.
%K A029572 nonn
%O A029572 0,6
%A A029572 _Rob Pratt_