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 A245791 Number of preferential arrangements of n labeled elements when at least k=6 elements per rank are required. 4

%I

%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 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

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Last modified September 25 19:04 EDT 2021. Contains 347659 sequences. (Running on oeis4.)