OFFSET
0,3
COMMENTS
Each node of the tree is a subset of the labeled set {1,...,n}. If the subset node is empty, it must have degree at least 3.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.26.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
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. Lecture Notes in Math., 829 (1980), 110-126. (Annotated scanned copy)
J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.
K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, 27 (1978), 309-318. (Annotated scanned copy)
N. J. A. Sloane, Transforms
FORMULA
MATHEMATICA
a[n_ /; n > 2] := 2^(n-1)*(n-2)!*Sum[ Binomial[n+k-2, n-2]*Sum[ (-1)^j*Binomial[k, j]*Sum[ ((-1)^l*2^(j-l)*Binomial[j, l]*(j-l)!*StirlingS1[n+j-l-2, j-l])/(n+j-l-2)!, {l, 0, j}], {j, 1, k}], {k, 1, n-2}]; a[0] = a[1] = 1; a[2] = 2; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Apr 10 2012, after Vladimir Kruchinin *)
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms, formula and comment from Christian G. Bower, Nov 15 1999
STATUS
approved