A213323 Number of permutations of n objects such that no four-element subset is preserved.

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.

Links

Table of n, a(n) for n=0..23.

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

Cf. A000166, A137482, A213322, A213324

Sequence in context: A138703 A106458 A354351 * A293016 A122685 A109581

Adjacent sequences: A213320 A213321 A213322 * A213324 A213325 A213326

Keyword

nonn

Author

Les Reid, Jun 08 2012

Status

approved