A245794 Number of preferential arrangements of n labeled elements when at least k=9 elements per rank are required.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 48621, 184757, 520677, 1293293, 2993565, 6626669, 14233965, 29938871, 62040891, 228000637831, 1914395677411, 10597881432571, 48446119334191, 197900630004571, 750527665784311, 2700730064112181

Offset

0,19

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! + x^8/8!). - Vaclav Kotesovec, Aug 02 2014

a(n) ~ n! / ((1+r^8/8!) * r^(n+1)), where r = 3.93616250913523371282009... 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! + r^8/8! = 0. - Vaclav Kotesovec, Aug 02 2014

Maple

a:= proc(n) option remember; `if`(n=0, 1,
       add(a(n-j)*binomial(n, j), j=9..n))
    end:
seq(a(n), n=0..40);

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^8/8!), {x, 0, 40}], x]*Range[0, 40]! (* Vaclav Kotesovec, Aug 02 2014 *)

Crossrefs

Cf. column k=9 of A245732.

Sequence in context: A172613 A172554 A244172 * A048341 A062204 A173780

Adjacent sequences: A245791 A245792 A245793 * A245795 A245796 A245797

Keyword

nonn

Author

Alois P. Heinz, Aug 01 2014

Status

approved