cp's OEIS Frontend

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.

A006680 Number of binary phylogenetic trees with n labels.

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%I A006680 M4427 #20 Jul 08 2025 16:52:29
%S A006680 1,1,7,45,465,5775,88515,1588545,32852925,768242475,20053670175,
%T A006680 577971719325,18230691904425,624676513836375,23106221910646875,
%U A006680 917643290676737625,38944796393877499125,1759004961887566267875
%N A006680 Number of binary phylogenetic trees with n labels.
%D A006680 Foulds, L. R.; Robinson, R. W. Enumeration of binary phylogenetic trees. Combinatorial mathematics, VIII (Geelong, 1980), pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. Math. Rev. 83a:05071.
%D A006680 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006680 L. R. Foulds and R. W. Robinson, <a href="/A006677/a006677.pdf">Enumeration of binary phylogenetic trees</a>, pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. (Annotated scanned copy)
%H A006680 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A006680 a(2) = 1, a(n) = A006678(n-1) + 2*(n-1)*A006678(n-2) - (n+1)*a(n-1) for n >= 3. - _Sean A. Irvine_, Jun 16 2017
%K A006680 nonn
%O A006680 2,3
%A A006680 _N. J. A. Sloane_
%E A006680 More terms and offset corrected by _Sean A. Irvine_, Jun 16 2017