cp's OEIS Frontend

A245792 Number of preferential arrangements of n labeled elements when at least k=7 elements per rank are required.

%I A245792 #9 Aug 02 2014 05:43:49
%S A245792 1,0,0,0,0,0,0,1,1,1,1,1,1,1,3433,12871,35751,87517,199785,436697,
%T A245792 927657,401005793,3296326113,17887397621,80157730101,321127444171,
%U A245792 1195366208091,4226755326331,486914893507831,6899197122043711,61532746814157691,436349292456987871
%N A245792 Number of preferential arrangements of n labeled elements when at least k=7 elements per rank are required.
%H A245792 Alois P. Heinz, <a href="/A245792/b245792.txt">Table of n, a(n) for n = 0..400</a>
%F A245792 E.g.f.: 1/(2 + x - exp(x) + x^2/2! + x^3/3! + x^4/4! + x^5/5! + x^6/6!). - _Vaclav Kotesovec_, Aug 02 2014
%F A245792 a(n) ~ n! / ((1+r^6/6!) * r^(n+1)), where r = 3.161936258680679649... 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! = 0. - _Vaclav Kotesovec_, Aug 02 2014
%p A245792 a:= proc(n) option remember; `if`(n=0, 1,
%p A245792        add(a(n-j)*binomial(n, j), j=7..n))
%p A245792     end:
%p A245792 seq(a(n), n=0..35);
%t A245792 CoefficientList[Series[1/(2 + x - E^x + x^2/2! + x^3/3! + x^4/4! + x^5/5! + x^6/6!),{x,0,40}],x]*Range[0,40]! (* _Vaclav Kotesovec_, Aug 02 2014 *)
%Y A245792 Cf. column k=7 of A245732.
%K A245792 nonn
%O A245792 0,15
%A A245792 _Alois P. Heinz_, Aug 01 2014