This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A034855 #49 Feb 09 2018 21:46:52
%S A034855 2,3,6,4,36,24,5,200,300,120,6,1170,3360,2520,720,7,7392,38850,43680,
%T A034855 22680,5040,8,50568,475776,757680,551040,221760,40320,9,372528,
%U A034855 6231960,13747104,12836880,7136640,2358720,362880,10,2936070,87530400,264181680
%N A034855 Triangle read by rows giving number of rooted labeled trees with n >= 2 nodes and height d >= 1.
%H A034855 Alois P. Heinz, <a href="/A034855/b034855.txt">Rows n = 2..101, flattened</a>
%H A034855 Marko Riedel, <a href="http://math.stackexchange.com/questions/1801039/">Counting the number of rooted trees of a certain height</a>
%H A034855 Marko Riedel, <a href="/A034855/a034855_1.maple.txt">Maple code for sequence (EGF)</a>
%H A034855 J. Riordan, <a href="http://www.research.ibm.com/journal/rd/045/ibmrd0405E.pdf">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478. [broken link]
%H A034855 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 A034855 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 A034855 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A034855 Riordan reference gives recurrence.
%e A034855 2;
%e A034855 3, 6;
%e A034855 4, 36, 24;
%e A034855 5, 200, 300, 120;
%e A034855 6, 1170, 3360, 2520, 720;
%e A034855 7, 7392, 38850, 43680, 22680, 5040;
%p A034855 gf:= proc(k) gf(k):= `if`(k=0, x, x*exp(gf(k-1))) end:
%p A034855 A:= proc(n, k) A(n, k):= n!*coeff(series(gf(k), x, n+1), x, n) end:
%p A034855 T:= (n, d)-> A(n, d) -A(n, d-1):
%p A034855 seq(seq(T(n, d), d=1..n-1), n=2..12); # _Alois P. Heinz_, Sep 21 2012
%t A034855 gf[k_] := gf[k] = If[k == 0, x, x*E^gf[k - 1]]; a[n_, k_] := n!*Coefficient[ Series[gf[k], {x, 0, n + 1}], x, n]; t[n_, d_] := a[n, d] - a[n, d - 1]; Table[t[n, d], {n, 2, 12}, {d, 1, n - 1}] // Flatten (* _Jean-François Alcover_, Jan 15 2013, translated from _Alois P. Heinz_'s Maple program *)
%Y A034855 Cf. A001854, A234953, A000435, A236396.
%K A034855 nonn,tabl,easy,nice
%O A034855 2,1
%A A034855 _N. J. A. Sloane_
%E A034855 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 27 2004