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A000551 Number of labeled rooted trees of height 2 with n nodes.

%I A000551 M4220 N1764 #41 Apr 17 2017 14:46:36
%S A000551 6,36,200,1170,7392,50568,372528,2936070,24617120,218521116,
%T A000551 2045278248,20112821274,207162957120,2228888801040,24989309310944,
%U A000551 291322555295886,3524580202643136,44176839081266340,572725044269255640
%N A000551 Number of labeled rooted trees of height 2 with n nodes.
%D A000551 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000551 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000551 Vincenzo Librandi, <a href="/A000551/b000551.txt">Table of n, a(n) for n = 3..200</a>
%H A000551 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 A000551 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A000551 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A000551 E.g.f.: x*(exp(x*exp(x))-exp(x)), cf. A074728. - _Vladeta Jovovic_, Jan 29 2008
%F A000551 a(n) = n*(n-1)*A074728(n-2). - _Sean A. Irvine_, Nov 21 2010
%p A000551 # ht(m) counts trees of height<=m; 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[ 4220 ] := n->count(ht(2),size=n)-count(ht(1),size=n): seq(M[ 4220 ](n), n=3..21);
%t A000551 a[n_] = n*(n-1)*Sum[k^(n-2-k)*Binomial[n-2, k-1], {k, n-2}]; Table[a[n], {n, 3, 21}] (* _Jean-François Alcover_, Jun 29 2011, after formula *)
%t A000551 With[{nn=30},Drop[CoefficientList[Series[x (Exp[x Exp[x]]-Exp[x]),{x,0,nn}], x] Range[0,nn]!,3]] (* _Harvey P. Dale_, Apr 17 2017 *)
%K A000551 nonn,nice,easy
%O A000551 3,1
%A A000551 _N. J. A. Sloane_
%E A000551 More terms from Flajolet and Zimmermann, Mar 15 1996