A006680 Number of binary phylogenetic trees with n labels. (Formerly M4427)

1, 1, 7, 45, 465, 5775, 88515, 1588545, 32852925, 768242475, 20053670175, 577971719325, 18230691904425, 624676513836375, 23106221910646875, 917643290676737625, 38944796393877499125, 1759004961887566267875

Offset

2,3

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

Table of n, a(n) for n=2..19.

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(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

Crossrefs

Sequence in context: A071971 A370253 A337553 * A197796 A197856 A205080

Adjacent sequences: A006677 A006678 A006679 * A006681 A006682 A006683

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms and offset corrected by Sean A. Irvine, Jun 16 2017

Status

approved