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%I #9 Aug 02 2014 05:44:40
%S 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,184757,705433,1998725,
%T 4992289,11618957,25852921,55791791,117832681,245039011,503891821,
%U 5552024604991,46933238932021,261680950107511,1205121760579981,4959685199012641,18947093053200193
%N Number of preferential arrangements of n labeled elements when at least k=10 elements per rank are required.
%H Alois P. Heinz, <a href="/A245795/b245795.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! + x^8/8! + x^9/9!). - _Vaclav Kotesovec_, Aug 02 2014
%F a(n) ~ n! / ((1+r^9/9!) * r^(n+1)), where r = 4.320434975980068857383128... 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! + r^8/8! + r^9/9! = 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=10..n))
%p end:
%p seq(a(n), n=0..40);
%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^8/8! + x^9/9!),{x,0,40}],x]*Range[0,40]! (* _Vaclav Kotesovec_, Aug 02 2014 *)
%Y Cf. column k=10 of A245732.
%K nonn
%O 0,21
%A _Alois P. Heinz_, Aug 01 2014
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