A213324 -id:A213324 - cp's OEIS frontend

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

Les Reid, Jun 08 2012

nonn

The limit as n -> infinity of a(n)/n! = (3+2*exp(1/2))/(2*exp(11/6)) or approximately 0.5034167572.

			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.

Cf. A000166, A137482, A213323, A213324.

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

E.g.f.:((x+x^2/2)*exp(-x-x^2/2-x^3/3)+exp(-x-x^3/3))/(1-x)

More terms from Michel Marcus, Aug 14 2013

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

Original entry on oeis.org

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

Les Reid, Jun 08 2012

nonn

The limit as n -> infinity of a(n)/n! = (13+9*exp(1/3))/(6*exp(25/12)) or approximately 0.5304422700.

			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.

Cf. A000166, A137482, A213322, A213324

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 */

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)

cp's OEIS Frontend

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

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