A006682 Number of binary phylogenetic trees with n labels.
1, 4, 20, 155, 1716, 24654, 434155, 9043990, 217457456, 5926620029, 180538177590, 6078622845750, 224156328707221, 8984765008810504, 388939866084222200, 18083736252080051435, 898779656769444326136, 47551736771345760732954
Offset: 2
Keywords
References
- 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.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- L. R. Foulds and R. W. Robinson, Enumeration of binary phylogenetic trees, pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. (Annotated scanned copy)
- Index entries for sequences related to trees
Formula
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
Extensions
More terms and offset corrected by Sean A. Irvine, Jun 16 2017