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A245793 Number of preferential arrangements of n labeled elements when at least k=8 elements per rank are required. 4

%I #9 Aug 02 2014 05:44:04

%S 1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,12871,48621,136137,335921,772617,

%T 1700273,3633105,7607297,9481216677,78911366771,433024685291,

%U 1961914734031,7943932891111,29871106149031,106624217245891,366332387265871,100783979161693411

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

%H Alois P. Heinz, <a href="/A245793/b245793.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! + x^6/6! + x^7/7!). - _Vaclav Kotesovec_, Aug 02 2014

%F 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 a:= proc(n) option remember; `if`(n=0, 1,

%p add(a(n-j)*binomial(n, j), j=8..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^6/6! + x^7/7!),{x,0,40}],x]*Range[0,40]! (* _Vaclav Kotesovec_, Aug 02 2014 *)

%Y Cf. column k=8 of A245732.

%K nonn

%O 0,17

%A _Alois P. Heinz_, Aug 01 2014

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)