cp's OEIS Frontend

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

%I A245794 #9 Aug 02 2014 05:44:25
%S A245794 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,48621,184757,520677,1293293,
%T A245794 2993565,6626669,14233965,29938871,62040891,228000637831,
%U A245794 1914395677411,10597881432571,48446119334191,197900630004571,750527665784311,2700730064112181
%N A245794 Number of preferential arrangements of n labeled elements when at least k=9 elements per rank are required.
%H A245794 Alois P. Heinz, <a href="/A245794/b245794.txt">Table of n, a(n) for n = 0..400</a>
%F A245794 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
%F A245794 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
%p A245794 a:= proc(n) option remember; `if`(n=0, 1,
%p A245794        add(a(n-j)*binomial(n, j), j=9..n))
%p A245794     end:
%p A245794 seq(a(n), n=0..40);
%t A245794 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 *)
%Y A245794 Cf. column k=9 of A245732.
%K A245794 nonn
%O A245794 0,19
%A A245794 _Alois P. Heinz_, Aug 01 2014