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%I
%S 1,1,1,2,3,6,11,19,31,52,85,140,228,370,594,954,1519,2412,3814,6006,
%T 9419,14726,22938,35612,55125,85065,130900,200875,307446,469342,
%U 714784,1085956,1646160,2489838,3757929,5660110,8508224,12764585,19114360,28570525,42629077
%N Number of n-node rooted identity trees of height at most 5.
%C A finite sequence with A038093(5) = 3211265 terms.
%H Alois P. Heinz, <a href="/A038084/b038084.txt">Table of n, a(n) for n = 1..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F Take Weigh transform of A038083 and shift right.
%p 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..42); # _Alois P. Heinz_, Sep 10 2008
%Y Cf. A038081-A038093.
%K nonn,fini,changed
%O 1,4
%A _Christian G. Bower_, Jan 04 1999.
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