%I #9 Aug 02 2014 05:43:30
%S 1,0,0,0,0,0,1,1,1,1,1,1,925,3433,9439,22881,51767,112269,17390049,
%T 140166497,749266977,3311021321,13091222301,48138992687,2477067794573,
%U 33549609515571,292811657874791,2040445353211231,12382874543793451,68436110449556971
%N Number of preferential arrangements of n labeled elements when at least k=6 elements per rank are required.
%H Alois P. Heinz, <a href="/A245791/b245791.txt">Table of n, a(n) for n = 0..400</a>
%F 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 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 a:= proc(n) option remember; `if`(n=0, 1,
%p add(a(n-j)*binomial(n, j), j=6..n))
%p end:
%p seq(a(n), n=0..35);
%t 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 Cf. column k=6 of A245732.
%K nonn
%O 0,13
%A _Alois P. Heinz_, Aug 01 2014