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%I #14 May 14 2016 14:50:38
%S 0,0,0,0,0,0,1,63,2282,62370,1428987,28979181,537306484,9302333040,
%T 152587968533,2396472657579,36320866824606,534421447961310,
%U 7670116319449039,107781064078390857,1487396442778796648,20208696810429799980,270879169288278532905
%N Expansion of x^k/Product_{t=k..2k} (1-tx) for k=6.
%C a(n) is also the number of forests of 6 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
%H Alois P. Heinz, <a href="/A143401/b143401.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f.: x^6/((1-6x)(1-7x)(1-8x)(1-9x)(1-10x)(1-11x)(1-12x)).
%F E.g.f.: exp(6*x)*((exp(x)-1)^6)/6!.
%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(6); seq(a(n), n=0..27);
%Y 6th column of A143395.
%K nonn
%O 0,8
%A _Alois P. Heinz_, Aug 12 2008