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%I #16 May 14 2016 14:53:42
%S 0,0,0,0,0,0,0,1,84,3990,141120,4138827,106469748,2484848080,
%T 53791898160,1096912870053,21307466872692,397605494092170,
%U 7173885616672320,125794299357058879,2152559266567924116,36065247772657686660,593280221500152370800
%N Expansion of x^k/Product_{t=k..2k} (1-tx) for k=7.
%C a(n) is also the number of forests of 7 labeled rooted trees of height at most 1, with n labels, where any root may contain >= 1 labels.
%H Alois P. Heinz, <a href="/A143402/b143402.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^7/((1-7x)(1-8x)(1-9x)(1-10x)(1-11x)(1-12x)(1-13x)(1-14x)).
%F E.g.f.: exp(7*x)*((exp(x)-1)^7)/7!.
%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(7): seq(a(n), n=0..30);
%Y 7th column of A143395.
%K nonn
%O 0,9
%A _Alois P. Heinz_, Aug 12 2008
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