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A038087 Number of n-node rooted identity trees of height at most 8.

%I A038087 #25 Dec 19 2015 10:00:19
%S A038087 1,1,1,2,3,6,12,25,52,112,238,503,1053,2194,4547,9406,19401,39965,
%T A038087 82189,168837,346380,709917,1453380,2972636,6074138,12400794,25295272,
%U A038087 51556337,104998985,213681811,434548933,883104930,1793484049,3640032699,7383188993
%N A038087 Number of n-node rooted identity trees of height at most 8.
%C A038087 A finite sequence with a very large number of terms, A038093(8). The sum of all terms is 2^(2^(2^(2^65536))).
%H A038087 Alois P. Heinz, <a href="/A038087/b038087.txt">Table of n, a(n) for n = 1..1000</a>
%H A038087 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A038087 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038087 Take Weigh transform of A038086 and shift right.
%p A038087 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@@5)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n],0)): seq(a(n), n=1..33);  # _Alois P. Heinz_, Sep 10 2008
%t A038087 Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 8] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y A038087 Cf. A038081-A038093.
%K A038087 nonn,fini
%O A038087 1,4
%A A038087 _Christian G. Bower_, Jan 04 1999