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%I M3461 N1408 #42 Feb 09 2018 21:43:19
%S 0,0,0,0,1,4,13,36,93,225,528,1198,2666,5815,12517,26587,55933,116564,
%T 241151,495417,1011950,2055892,4157514,8371318,16792066,33564256,
%U 66875221,132849983,263192599,520087551,1025295487,2016745784,3958608430,7754810743
%N Number of n-node rooted trees of height 4.
%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 Alois P. Heinz, <a href="/A000299/b000299.txt">Table of n, a(n) for n = 1..1000</a> (first 200 terms from N. J. A. Sloane)
%H F. Harary & R. W. Robinson, <a href="/A000108/a000108_18.pdf">The number of achiral trees</a>, Jnl. Reine Angewandte Mathematik 278 (1975), 322-335. (Annotated scanned copy)
%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 J. Riordan, <a href="/A007401/a007401_8.pdf">The enumeration of trees by height and diameter</a>, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
%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 Cf. A001384-A001383. - _Christian G. Bower_
%p For Maple program see link in A000235.
%t f[n_] := Nest[CoefficientList[Series[Product[1/(1 - x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x] &, {1}, n];f[4]-f[3] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y Column h=4 of A034781.
%K nonn
%O 1,6
%A _N. J. A. Sloane_
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