A245793 Number of preferential arrangements of n labeled elements when at least k=8 elements per rank are required.

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 12871, 48621, 136137, 335921, 772617, 1700273, 3633105, 7607297, 9481216677, 78911366771, 433024685291, 1961914734031, 7943932891111, 29871106149031, 106624217245891, 366332387265871, 100783979161693411

Offset

0,17

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Formula

E.g.f.: 1/(2 + x - exp(x) + x^2/2! + x^3/3! + x^4/4! + x^5/5! + x^6/6! + x^7/7!). - Vaclav Kotesovec, Aug 02 2014

a(n) ~ n! / ((1+r^7/7!) * r^(n+1)), where r = 3.550140591759854453327299... is the root of the equation 2 + r - exp(r) + r^2/2! + r^3/3! + r^4/4! + r^5/5! + r^6/6! + r^7/7! = 0. - Vaclav Kotesovec, Aug 02 2014

Maple

a:= proc(n) option remember; `if`(n=0, 1,
       add(a(n-j)*binomial(n, j), j=8..n))
    end:
seq(a(n), n=0..35);

Mathematica

CoefficientList[Series[1/(2 + x - E^x + x^2/2! + x^3/3! + x^4/4! + x^5/5! + x^6/6! + x^7/7!), {x, 0, 40}], x]*Range[0, 40]! (* Vaclav Kotesovec, Aug 02 2014 *)

Crossrefs

Cf. column k=8 of A245732.

Sequence in context: A172560 A031805 A244171 * A251922 A184453 A233936

Adjacent sequences: A245790 A245791 A245792 * A245794 A245795 A245796

Keyword

nonn

Author

Alois P. Heinz, Aug 01 2014

Status

approved