A213323 - OEIS

%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