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 A038084 Number of n-node rooted identity trees of height at most 5. 4

%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..50); # _Alois P. Heinz_, Sep 10 2008

%t Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]],{i,1,Length[#]}],{x,0,40}],x]&,{1},5] (* _Geoffrey Critzer_, Aug 01 2013 *)

%Y Cf. A038081-A038093.

%K nonn,fini

%O 1,4

%A _Christian G. Bower_, Jan 04 1999

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