OFFSET
0,3
COMMENTS
The limit as n -> infinity of a(n)/n! = (13+9*exp(1/3))/(6*exp(25/12)) or approximately 0.5304422700.
FORMULA
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)
EXAMPLE
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.
PROG
(PARI)
x='x+O('x^66);
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);
Vec(serlaplace(egf))
/* Joerg Arndt, Jun 09 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Les Reid, Jun 08 2012
STATUS
approved