%I A143404
%S A143404 0,0,0,0,0,0,0,0,0,1,135,10065,547965,24336312,934863930,32189799070,
%T A143404 1017281878470,30001945084683,835898091070185,22206607023852615,
%U A143404 566594907018764715,13964270139973201114,333991935681805199700
%N A143404 Expansion of x^k/Prod_{t=k..2k}(1-tx) for k=9.
%C A143404 a(n) is also the number of forests of 9 labeled rooted trees of height 
               at most 1 with n labels, where any root may contain >= 1 labels.
%H A143404 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A143404 G.f.: x^9/ ((1-9x)(1-10x)(1-11x)(1-12x)(1-13x)(1-14x)(1-15x)(1-16x)(1-17x)(1-18*x)).
%p A143404 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(9); seq (a(n), 
               n=0..27);
%Y A143404 9th column of A143395.
%Y A143404 Sequence in context: A157734 A061073 A004005 this_sequence A051028 A076011 
               A132054
%Y A143404 Adjacent sequences: A143401 A143402 A143403 this_sequence A143405 A143406 
               A143407
%K A143404 nonn
%O A143404 0,11
%A A143404 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 12 2008