1,2

Each node is a subset of the labeled set {1,...,n}. If the subset node is empty, it must have at least two children.

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

J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.

L. R. Foulds and R. W. Robinson, Determining the asymptotic number of phylogenetic trees, pp. 110-126 of Combinatorial Mathematics VII (Newcastle, August 1979), ed. R. W. Robinson, G. W. Southern and W. D. Wallis. Lect. Notes in Math., 829. Springer, 1980.

F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.26.

T. D. Noe, Table of n, a(n) for n=1..30

Index entries for sequences related to trees

Index entries for sequences related to rooted trees

E.g.f.: -1/2 - LambertW ( - exp( -1/2 + x) / 2 ).

E.g.f.: A(x) = 1 + Integral A(x)*(1 + A(x))^2 dx. [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 06 2008]

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(A*(1+A+x*O(x^n))^2)); n!*polcoeff(A, n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 06 2008]

Cf. A005640.

John Layman (layman(AT)calvin.math.vt.edu) observes that this is the Stirling transform of A005264.

Sequence in context: A005263 A113131 A127670 this_sequence A140178 A088991 A009668

Adjacent sequences: A005169 A005170 A005171 this_sequence A005173 A005174 A005175

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).