cp's OEIS Frontend

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

%I A245793 #9 Aug 02 2014 05:44:04
%S A245793 1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,12871,48621,136137,335921,772617,
%T A245793 1700273,3633105,7607297,9481216677,78911366771,433024685291,
%U A245793 1961914734031,7943932891111,29871106149031,106624217245891,366332387265871,100783979161693411
%N A245793 Number of preferential arrangements of n labeled elements when at least k=8 elements per rank are required.
%H A245793 Alois P. Heinz, <a href="/A245793/b245793.txt">Table of n, a(n) for n = 0..400</a>
%F A245793 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
%F A245793 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
%p A245793 a:= proc(n) option remember; `if`(n=0, 1,
%p A245793        add(a(n-j)*binomial(n, j), j=8..n))
%p A245793     end:
%p A245793 seq(a(n), n=0..35);
%t A245793 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 *)
%Y A245793 Cf. column k=8 of A245732.
%K A245793 nonn
%O A245793 0,17
%A A245793 _Alois P. Heinz_, Aug 01 2014