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A213322 Number of permutations of n objects such that no three-element subset is preserved. 2
1, 1, 2, 0, 9, 54, 459, 2568, 20145, 176076, 1833741, 20148336, 241870617, 3132196560, 43874128089, 658195206264, 10533823597089, 179062417518768, 3223079582143185, 61237777946016096, 1224762717659002281, 25720036368344942616, 565841009719801635777 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The limit as n -> infinity of a(n)/n! = (3+2*exp(1/2))/(2*exp(11/6)) or approximately 0.5034167572.
LINKS
FORMULA
E.g.f.:((x+x^2/2)*exp(-x-x^2/2-x^3/3)+exp(-x-x^3/3))/(1-x)
EXAMPLE
Example: For n=5 the only permutations that fix no three-element subset are the 24 5-cycles and the 30 4-cycles, therefore a(5)=54.
PROG
(PARI) lista(nn) = {x=xx+O(xx^nn); egf=((x+x^2/2)*exp(-x-x^2/2-x^3/3)+exp(-x-x^3/3))/(1-x); Vec(serlaplace(egf)) ; } \\ Michel Marcus, Aug 14 2013
CROSSREFS
Sequence in context: A037996 A299626 A002741 * A368703 A345048 A151887
KEYWORD
nonn
AUTHOR
Les Reid, Jun 08 2012
EXTENSIONS
More terms from Michel Marcus, Aug 14 2013
STATUS
approved

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Last modified April 14 12:23 EDT 2024. Contains 371661 sequences. (Running on oeis4.)