

A006678


Number of planted binary phylogenetic trees with n labels.
(Formerly M4232)


1



0, 1, 1, 6, 39, 390, 4815, 73080, 1304415, 26847450, 625528575, 16279193700, 468022452975, 14731683916950, 503880434632575, 18609309606888000, 738057377647965375, 31286068076704691250, 1411602439003747365375, 67543694966494692445500, 3416288904242387117319375
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


REFERENCES

Foulds, L. R.; Robinson, R. W. Enumeration of binary phylogenetic trees. Combinatorial mathematics, VIII (Geelong, 1980), pp. 187202, Lecture Notes in Math., 884, Springer, BerlinNew 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=0..20.
L. R. Foulds and R. W. Robinson, Enumeration of binary phylogenetic trees, pp. 187202, Lecture Notes in Math., 884, Springer, BerlinNew York, 1981. (Annotated scanned copy)
Plouffe, Simon, Master's Thesis, Uqam, 1992.
Index entries for sequences related to rooted trees
Index entries for sequences related to trees


FORMULA

E.g.f.: (1+(12*x2*x^2)^(1/2))/(1+x), Simon Plouffe in his Master's Thesis, Uqam 1992.
a(n) ~ sqrt(62*sqrt(3)) * (1+sqrt(3))^(n1) * n^(n1) / exp(n).  Vaclav Kotesovec, Oct 01 2013


MATHEMATICA

CoefficientList[Series[(1+(12*x2*x^2)^(1/2))/(1+x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)


CROSSREFS

Sequence in context: A031972 A308861 A124577 * A252761 A145709 A280006
Adjacent sequences: A006675 A006676 A006677 * A006679 A006680 A006681


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Simon Plouffe


STATUS

approved



