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

0,3

Comments

The limit as n -> infinity of a(n)/n! = (35-24*exp(1/4)+24*exp(1/3)+24*exp(7/12)+24*exp(3/4))/(24*exp[(137/60)) or approximately 0.5585422951.

Links

Table of n, a(n) for n=0..24.

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)

Example

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.

Prog

(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 */

Crossrefs

Cf. A000166, A137482, A213322, A213323

Sequence in context: A020122 A327426 A086554 * A007672 A322255 A084337

Adjacent sequences: A213321 A213322 A213323 * A213325 A213326 A213327

Keyword

nonn

Author

Les Reid, Jun 08 2012

Status

approved