A213324 Number of permutations of n objects such that no five-element subset is preserved.

1, 1, 2, 6, 24, 0, 265, 2260, 20145, 200240, 2492225, 23163480, 270877705, 3449462080, 48030998625, 713129276000, 11685451112225, 198919432944000, 3585292622812225, 68053546078588000, 1360638669122771625, 28525836193802883200, 627637954389517169825, 14435957818250131813200, 346518764145610187160625

Offset: 0

Author

Les Reid, Jun 08 2012

Keywords

• nonn

Comments

Limit_{n->oo} a(n)/n! = (35-24*exp(1/4)+24*exp(1/3)+24*exp(7/12)+24*exp(3/4))/(24*exp(137/60)) = 0.5585422951...

Examples

			For n=6 the only permutations that fix no five-element subset are the 120 6-cycles, the 90 products of a 4-cycle and a 2-cycle, the 40 products of two 3-cycles, and the 15 products of three 2-cycles, therefore a(5)=265.
		

Crossrefs

Cf. A000166, A137482, A213322, A213323

Programs

PARI

x='x+O('x^66);
egf=((x^2/2+2*x^3/3+7*x^4/24)*exp(-x-x^2/2-x^3/3-x^4/4-x^5/5)+x*exp(-x-x^2/2-x^4/4-x^5/5)+exp(-x-x^2/2-x^5/5)+exp(-x-x^3/3-x^5/5)-exp(-x-x^2/2-x^3/3-x^5/5))/(1-x);
Vec(serlaplace(egf))
/* Joerg Arndt, Jun 09 2012 */

Formula

E.g.f.: ((x^2/2+2*x^3/3+7*x^4/24)*exp(-x-x^2/2-x^3/3-x^4/4-x^5/5)+x*exp(-x-x^2/2-x^4/4-x^5/5)+exp(-x-x^2/2-x^5/5)+exp(-x-x^3/3-x^5/5)-exp(-x-x^2/2-x^3/3-x^5/5))/(1-x).