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%I #15 May 14 2016 14:53:19
%S 0,0,0,0,0,0,0,0,1,108,6510,289080,10550067,335170836,9597839680,
%T 253489991040,6275077781973,147318890173884,3309320153700210,
%U 71623038281001480,1501654449863348119,30633757929391948452,610246760750629071300,11906371167306982146000
%N Expansion of x^k/Product_{t=k..2k} (1-tx) for k=8.
%C a(n) is also the number of forests of 8 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
%H Alois P. Heinz, <a href="/A143403/b143403.txt">Table of n, a(n) for n = 0..250</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f.: x^8/((1-8x)(1-9x)(1-10x)(1-11x)(1-12x)(1-13x)(1-14x)(1-15x)(1-16x)).
%F E.g.f.: exp(8*x)*((exp(x)-1)^8)/8!.
%p a:= proc(k::nonnegint) local M; M:= Matrix(k+1, (i,j)-> if (i=j-1) then 1 elif j=1 then [seq(-1* coeff(product(1-t*x, t=k..2*k), x,u), u=1..k+1)][i] else 0 fi); p-> (M^p)[1,k+1] end(8); seq(a(n), n=0..27);
%Y 8th column of A143395.
%K nonn
%O 0,10
%A _Alois P. Heinz_, Aug 12 2008
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