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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 15:01 EDT 2022. Contains 356026 sequences. (Running on oeis4.)