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A038085 Number of n-node rooted identity trees of height at most 6.

%I A038085 #23 Dec 19 2015 09:59:52
%S A038085 1,1,1,2,3,6,12,24,45,85,157,289,529,969,1764,3208,5807,10493,18901,
%T A038085 33977,60919,109019,194662,346940,617148,1095884,1942576,3437834,
%U A038085 6074239,10716076,18877025,33205498,58328831,102323302,179267087,313674445,548183968
%N A038085 Number of n-node rooted identity trees of height at most 6.
%C A038085 The number of terms is A038093(6), a number that is too large to write down!
%H A038085 Alois P. Heinz, <a href="/A038085/b038085.txt">Table of n, a(n) for n = 1..1000</a>
%H A038085 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A038085 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038085 Take Weigh transform of A038084 and shift right.
%p A038085 weigh:= proc(p) proc(n) `if`(n<0, 1, coeff(mul((1+x^k)^p(k), k=1..n), x,n)) end end: wsh:= p-> n-> weigh(p)(n-1): a:= (wsh@@3)(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 A038085 Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 6] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y A038085 Cf. A038081-A038093.
%K A038085 nonn,fini
%O A038085 1,4
%A A038085 _Christian G. Bower_, Jan 04 1999