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 A213324 #13 Oct 27 2024 04:16:05
%S A213324 1,1,2,6,24,0,265,2260,20145,200240,2492225,23163480,270877705,
%T A213324 3449462080,48030998625,713129276000,11685451112225,198919432944000,
%U A213324 3585292622812225,68053546078588000,1360638669122771625,28525836193802883200,627637954389517169825,14435957818250131813200,346518764145610187160625
%N A213324 Number of permutations of n objects such that no five-element subset is preserved.
%C A213324 Limit_{n->oo} a(n)/n! = (35-24*exp(1/4)+24*exp(1/3)+24*exp(7/12)+24*exp(3/4))/(24*exp(137/60)) = 0.5585422951...
%F A213324 E.g.f.: ((x^2/2+2*x^3/3+7*x^4/24)*exp(-x-x^2/2-x^3/3-x^4/4-x^5/5)+x*exp(-x-x^2/2-x^4/4-x^5/5)+exp(-x-x^2/2-x^5/5)+exp(-x-x^3/3-x^5/5)-exp(-x-x^2/2-x^3/3-x^5/5))/(1-x).
%e A213324 For n=6 the only permutations that fix no five-element subset are the 120 6-cycles, the 90 products of a 4-cycle and a 2-cycle, the 40 products of two 3-cycles, and the 15 products of three 2-cycles, therefore a(5)=265.
%o A213324 (PARI)
%o A213324 x='x+O('x^66);
%o A213324 egf=((x^2/2+2*x^3/3+7*x^4/24)*exp(-x-x^2/2-x^3/3-x^4/4-x^5/5)+x*exp(-x-x^2/2-x^4/4-x^5/5)+exp(-x-x^2/2-x^5/5)+exp(-x-x^3/3-x^5/5)-exp(-x-x^2/2-x^3/3-x^5/5))/(1-x);
%o A213324 Vec(serlaplace(egf))
%o A213324 /* _Joerg Arndt_, Jun 09 2012 */
%Y A213324 Cf. A000166, A137482, A213322, A213323
%K A213324 nonn
%O A213324 0,3
%A A213324 _Les Reid_, Jun 08 2012