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 A036376 #23 Oct 29 2020 03:26:07
%S A036376 1,1,1,2,4,8,17,39,89,210,498,1185,2813,6664,15707,36886,86259,201003,
%T A036376 466788,1080825,2495565,5747664,13206253,30276788,69267205,158155198,
%U A036376 360422113,819873747,1861732042,4220347570,9551287776
%N A036376 Number of ternary rooted trees with n nodes and height at most 8.
%H A036376 Sean A. Irvine, <a href="/A036376/b036376.txt">Table of n, a(n) for n = 0..3280</a>
%H A036376 E. M. Rains and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/cayley.html">On Cayley's Enumeration of Alkanes (or 4-Valent Trees)</a>, J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.
%H A036376 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A036376 If T_i(z) = g.f. for ternary trees of height at most i, T_{i+1}(z)=1+z*(T_i(z)^3/6+T_i(z^2)*T_i(z)/2+T_i(z^3)/3); T_0(z) = 1.
%t A036376 T[0] = {1}; T[n_] := T[n] = Module[{f, g}, f[z_] := Sum[T[n - 1][[i]]*z^(i - 1), {i, 1, Length[T[n - 1]]}]; g = 1 + z*(f[z]^3/6 + f[z^2]*f[z]/2 + f[z^3]/3); CoefficientList[g, z]]; A036376 = T[8][[1 ;; 40]] (* _Jean-François Alcover_, Jan 19 2016, after _Alois P. Heinz_ (A036370) *)
%Y A036376 Cf. A036370.
%K A036376 nonn,fini,full
%O A036376 0,4
%A A036376 _N. J. A. Sloane_, E. M. Rains (rains(AT)caltech.edu)