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A038086 Number of n-node rooted identity trees of height at most 7.

%I A038086 #24 Dec 19 2015 10:00:03
%S A038086 1,1,1,2,3,6,12,25,51,105,211,421,832,1641,3224,6328,12382,24200,
%T A038086 47197,91915,178683,346897,672443,1301850,2517078,4860938,9376300,
%U A038086 18066270,34772627,66859667,128427832,246456677,472519632,905131358,1732313955,3312661001
%N A038086 Number of n-node rooted identity trees of height at most 7.
%C A038086 The number of terms is A038093(7), a number that is too large to write down!
%H A038086 Alois P. Heinz, <a href="/A038086/b038086.txt">Table of n, a(n) for n = 1..1000</a>
%H A038086 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A038086 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038086 Take Weigh transform of A038085 and shift right.
%p A038086 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): a:= (wsh@@4)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..40);  # _Alois P. Heinz_, Sep 10 2008
%t A038086 Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 7] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y A038086 Cf. A038081-A038093.
%K A038086 nonn,fini
%O A038086 1,4
%A A038086 _Christian G. Bower_, Jan 04 1999