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A245794 Number of preferential arrangements of n labeled elements when at least k=9 elements per rank are required. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)