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 A036372 #17 Jan 19 2016 03:19:16
%S A036372 1,1,1,2,4,7,12,20,31,47,70,99,137,184,239,300,369,432,498,551,594,
%T A036372 614,624,601,570,514,453,378,312,238,181,128,89,56,37,20,12,6,3,1,1
%N A036372 Number of ternary rooted trees with n nodes and height at most 4.
%H A036372 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A036372 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 A036372 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]]; A036372 = T[4] (*_Jean-François Alcover_, Jan 19 2016, after _Alois P. Heinz_ (A036370) *)
%Y A036372 Cf. A036370.
%K A036372 nonn,full,fini
%O A036372 0,4
%A A036372 _N. J. A. Sloane_, E. M. Rains (rains(AT)caltech.edu)