login
Number of binary phylogenetic trees with n labels.
(Formerly M3571)
0

%I M3571 #16 Jan 10 2018 16:11:34

%S 1,4,20,155,1716,24654,434155,9043990,217457456,5926620029,

%T 180538177590,6078622845750,224156328707221,8984765008810504,

%U 388939866084222200,18083736252080051435,898779656769444326136,47551736771345760732954

%N Number of binary phylogenetic trees with n labels.

%D 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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(n) = Sum_{k=2..n} S(n, k) * A006680(k) where S(n, k) are Stirling numbers of the second kind. - _Sean A. Irvine_, Jun 16 2017

%K nonn

%O 2,2

%A _N. J. A. Sloane_.

%E More terms and offset corrected by _Sean A. Irvine_, Jun 16 2017