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 A000673 M0355 N0133 #32 Dec 19 2020 03:13:00 %S A000673 0,0,1,0,1,1,2,2,6,8,18,30,67,127,275,551,1192,2507,5475,11820,26007, %T A000673 57077,126686,281625,630660,1416116,3195784,7232624,16430563,37429146, %U A000673 85528079,195940960,450074270,1036226173,2391193488,5529420585 %N A000673 Number of bicentered 3-valent (or boron, or binary) trees with n nodes. %D A000673 A. Cayley, On the analytical forms called trees, with application to the theory of chemical combinations, Reports British Assoc. Advance. Sci. 45 (1875), 257-305 = Math. Papers, Vol. 9, 427-460 (see p. 451). %D A000673 R. C. Read, personal communication. %D A000673 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A000673 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A000673 Nicolas Broutin and Philippe Flajolet, <a href="https://doi.org/10.1002/rsa.20393">The distribution of height and diameter in random non-plane binary trees</a>, Random Struct. Algorithms 41, No. 2, 215-252 (2012). %H A000673 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 A000673 R. C. Read, <a href="/A000684/a000684_1.pdf">Letter to N. J. A. Sloane, Oct. 29, 1976</a> %H A000673 <a href="/index/Tra#trees">Index entries for sequences related to trees</a> %t A000673 n = 50; (* algorithm from Rains and Sloane *) %t A000673 S2[f_,h_,x_] := f[h,x]^2/2 + f[h,x^2]/2; %t A000673 T[-1,z_] := 1; T[h_,z_] := T[h,z] = Table[z^k, {k,0,n}].Take[CoefficientList[z^(n+1) + 1 + S2[T,h-1,z]z, z], n+1]; %t A000673 Sum[Take[CoefficientList[z^(n+1) + (T[h,z] - T[h-1,z])^2/2 + (T[h,z^2] - T[h-1,z^2])/2, z],n+1], {h,0,n/2}] (* _Robert A. Russell_, Sep 15 2018 *) %Y A000673 A000672 = A000673 + A000675. Cf. A000022, A000200, A000602. %K A000673 nonn,easy,nice %O A000673 0,7 %A A000673 _N. J. A. Sloane_