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A213323
Number of permutations of n objects such that no four-element subset is preserved.
2
1, 1, 2, 6, 0, 44, 304, 2568, 26704, 200240, 1931616, 20849696, 246556672, 3300906816, 46382446720, 695413794944, 11120648673024, 188600719094528, 3394592207824384, 64513420630110720, 1290420198709682176, 27102196040419214336, 596237419436696543232, 13713106494042086045696
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