A213322 Number of permutations of n objects such that no three-element subset is preserved.

1, 1, 2, 0, 9, 54, 459, 2568, 20145, 176076, 1833741, 20148336, 241870617, 3132196560, 43874128089, 658195206264, 10533823597089, 179062417518768, 3223079582143185, 61237777946016096, 1224762717659002281, 25720036368344942616, 565841009719801635777

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

Table of n, a(n) for n=0..22.

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

Cf. A000166, A137482, A213323, A213324.

Sequence in context: A037996 A299626 A002741 * A368703 A345048 A151887

Adjacent sequences: A213319 A213320 A213321 * A213323 A213324 A213325

Keyword

nonn

Author

Les Reid, Jun 08 2012

Extensions

More terms from Michel Marcus, Aug 14 2013

Status

approved