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%I #23 Dec 19 2015 10:00:52
%S 1,4,9,18,34,61,108,187,318,528,871,1417,2288,3662,5825,9203,14471,
%T 22639,35266,54725,84607,130379,200287,306787,468607,713970,1085060,
%U 1645181,2488771,3756778,5658871,8506900,12763178,19112874,28568961,42627442,63493739
%N Number of n-node rooted identity trees of height 5.
%C The number of terms with a(n)>0 is A038093(5)-5 = 3211260. - _Alois P. Heinz_, Sep 22 2013
%H Alois P. Heinz, <a href="/A038089/b038089.txt">Table of n, a(n) for n = 6..1000</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038084 - A038083.
%p 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@@2)(f)-wsh(f): seq(a(n), n=6..40); # _Alois P. Heinz_, Sep 10 2008
%t f[n_]:=Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]],{i,1,Length[#]}],{x,0,50}],x]&,{1},n];Drop[f[5]-PadRight[f[4], Length[f[5]]],5] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y Cf. A038081-A038093.
%Y Column k=5 of A227819.
%K nonn,fini
%O 6,2
%A _Christian G. Bower_, Jan 04 1999
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