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%I M4525 N1918 #32 Jul 08 2017 03:15:58
%S 0,0,0,0,0,0,0,0,1,8,43,188,728,2593,8706,27961,86802,262348,776126,
%T 2256418,6466614,18311915,51334232,142673720,393611872,1078955836,
%U 2941029334,7977065816,21541492856,57942770689,155304829763,414934057486
%N Number of n-node rooted trees of height 8.
%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 N. J. A. Sloane, <a href="/A000429/b000429.txt">Table of n, a(n) for n=1..200</a>
%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 a(n) = A034825(n) - A034824(n). - _Christian G. Bower_
%p For Maple program see link in A000235.
%t b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1 || k < 1, 0, Sum[ Binomial[b[i - 1, i - 1, k - 1] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]]; a[n_] := b[n - 1, n - 1, 8] - b[n - 1, n - 1, 7]; Array[a, 40] (* _Jean-François Alcover_, Feb 08 2016, after _Alois P. Heinz_ in A034781 *)
%Y Column h=8 of A034781.
%K nonn
%O 1,10
%A _N. J. A. Sloane_
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