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A245791 Number of preferential arrangements of n labeled elements when at least k=6 elements per rank are required.

%I A245791 #9 Aug 02 2014 05:43:30
%S A245791 1,0,0,0,0,0,1,1,1,1,1,1,925,3433,9439,22881,51767,112269,17390049,
%T A245791 140166497,749266977,3311021321,13091222301,48138992687,2477067794573,
%U A245791 33549609515571,292811657874791,2040445353211231,12382874543793451,68436110449556971
%N A245791 Number of preferential arrangements of n labeled elements when at least k=6 elements per rank are required.
%H A245791 Alois P. Heinz, <a href="/A245791/b245791.txt">Table of n, a(n) for n = 0..400</a>
%F A245791 E.g.f.: 1/(2 + x - exp(x) + x^2/2! + x^3/3! + x^4/4! + x^5/5!). - _Vaclav Kotesovec_, Aug 02 2014
%F A245791 a(n) ~ n! / ((1+r^5/5!) * r^(n+1)), where r = 2.77092853312194416389... is the root of the equation 2 + r - exp(r) + r^2/2! + r^3/3! + r^4/4! + r^5/5! = 0. - _Vaclav Kotesovec_, Aug 02 2014
%p A245791 a:= proc(n) option remember; `if`(n=0, 1,
%p A245791        add(a(n-j)*binomial(n, j), j=6..n))
%p A245791     end:
%p A245791 seq(a(n), n=0..35);
%t A245791 CoefficientList[Series[1/(2 + x - E^x + x^2/2! + x^3/3! + x^4/4! + x^5/5!),{x,0,30}],x]*Range[0,30]! (* _Vaclav Kotesovec_, Aug 02 2014 *)
%Y A245791 Cf. column k=6 of A245732.
%K A245791 nonn
%O A245791 0,13
%A A245791 _Alois P. Heinz_, Aug 01 2014