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%I M5159 N2241 #29 Apr 03 2017 04:23:25
%S 24,300,3360,38850,475776,6231960,87530400,1316954430,21173760960,
%T 362670636900,6596214691248,126980000240730,2579214238608000,
%U 55118036257959600,1235935135837111104,29009023670878484598
%N Number of labeled rooted trees of height 3 with n nodes.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. Riordan, <a href="http://dx.doi.org/10.1147/rd.45.0473">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F E.g.f.: x*(exp(x*exp(x*exp(x)))-exp(x*exp(x))). - _Vladeta Jovovic_, Jan 29 2008
%p ht := proc(m) local i; [ T0,{seq(T.i=Prod(Z,Set(T.(i+1))),i=0..m-1),T.m=Z},labeled ] end: M[ 5159 ] := n -> count(ht(3),size=n)-count(ht(2),size=n): seq(M[ 5159 ](n), n=4..19);
%t With[{nn=20},Drop[CoefficientList[Series[x(Exp[x Exp[x Exp[x]]]- Exp[x Exp[x]]),{x,0,nn}],x]Range[0,nn]!,4]] (* _Harvey P. Dale_, Oct 01 2011 *)
%K nonn,easy,nice
%O 4,1
%A _N. J. A. Sloane_
%E More terms from _Paul Zimmermann_, Mar 15 1996
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