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%I #6 Jun 09 2012 06:50:34
%S 1,1,2,6,0,44,304,2568,26704,200240,1931616,20849696,246556672,
%T 3300906816,46382446720,695413794944,11120648673024,188600719094528,
%U 3394592207824384,64513420630110720,1290420198709682176,27102196040419214336,596237419436696543232,13713106494042086045696
%N Number of permutations of n objects such that no four-element subset is preserved.
%C The limit as n -> infinity of a(n)/n! = (13+9*exp(1/3))/(6*exp(25/12)) or approximately 0.5304422700.
%F E.g.f.: ((x+x^2/2+2*x^3/3)*exp(-x-x^2/2-x^3/3-x^4/4)+(1+x^2/2)*exp(-x-x^2/2-x^4/4))/(1-x)
%e Example: For n=5 the only permutations that fix no four-element subset are the 24 5-cycles and the 20 products of a 3-cycle and a 2-cycle, therefore a(5)=44.
%o (PARI)
%o x='x+O('x^66);
%o egf=((x+x^2/2+2*x^3/3)*exp(-x-x^2/2-x^3/3-x^4/4)+(1+x^2/2)*exp(-x-x^2/2-x^4/4))/(1-x);
%o Vec(serlaplace(egf))
%o /* _Joerg Arndt_, Jun 09 2012 */
%Y Cf. A000166, A137482, A213322, A213324
%K nonn
%O 0,3
%A _Les Reid_, Jun 08 2012