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A038084 Number of n-node rooted identity trees of height at most 5.

%I A038084 #26 Dec 19 2015 09:59:40
%S A038084 1,1,1,2,3,6,11,19,31,52,85,140,228,370,594,954,1519,2412,3814,6006,
%T A038084 9419,14726,22938,35612,55125,85065,130900,200875,307446,469342,
%U A038084 714784,1085956,1646160,2489838,3757929,5660110,8508224,12764585,19114360,28570525,42629077
%N A038084 Number of n-node rooted identity trees of height at most 5.
%C A038084 A finite sequence with A038093(5) = 3211265 terms.
%H A038084 Alois P. Heinz, <a href="/A038084/b038084.txt">Table of n, a(n) for n = 1..1000</a>
%H A038084 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A038084 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A038084 Take Weigh transform of A038083 and shift right.
%p A038084 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@@2)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..50); # _Alois P. Heinz_, Sep 10 2008
%t A038084 Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]],{i,1,Length[#]}],{x,0,40}],x]&,{1},5] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y A038084 Cf. A038081-A038093.
%K A038084 nonn,fini
%O A038084 1,4
%A A038084 _Christian G. Bower_, Jan 04 1999