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A038091 Number of n-node rooted identity trees of height 7.

%I A038091 #25 Dec 19 2015 10:01:27
%S A038091 1,6,20,54,132,303,672,1460,3120,6575,13707,28296,57938,117764,237878,
%T A038091 477781,954910,1899930,3765054,7433724,14628436,28698388,56143591,
%U A038091 109550807,213251179,414190801,802808056,1553046868,2998986556,5781366468,11127506290
%N A038091 Number of n-node rooted identity trees of height 7.
%C A038091 The number of terms with a(n)>0 is A038093(7) - 7. - _Alois P. Heinz_, Sep 22 2013
%H A038091 Alois P. Heinz, <a href="/A038091/b038091.txt">Table of n, a(n) for n = 8..1000</a>
%H A038091 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038091 A038086 - A038085.
%p A038091 weigh:= proc(p) proc(n) local x,k; coeff(series(mul((1+x^k)^p(k), k=1..n), x,n+1), x,n) end end: wsh:= p-> n-> weigh(p)(n-1): f:= n-> `if`(n>0 and n<12, [1$3,2$5,1$3][n], 0): a:= (wsh@@4)(f)-(wsh@@3)(f): seq(a(n), n=8..36);  # _Alois P. Heinz_, Sep 10 2008
%t A038091 f[n_]:=Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]],{i,1,Length[#]}],{x,0,50}],x]&,{1},n];Drop[f[7]-PadRight[f[6],Length[f[7]]],7] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y A038091 Cf. A038081-A038093.
%Y A038091 Column k=7 of A227819.
%K A038091 nonn,fini
%O A038091 8,2
%A A038091 _Christian G. Bower_, Jan 04 1999