OFFSET
0,5
COMMENTS
Also, number of unrooted multifurcating tree shapes with n leaves [see Felsenstein].
REFERENCES
M. Cropper, J. Combin. Math. Combin. Comp., Vol. 24 (1997), 177-184.
Joseph Felsenstein, Inferring Phylogenies. Sinauer Associates, Inc., 2004, p. 33 (Beware errors!).
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 62.
S. B. Nadler Jr., Continuum Theory, Academic Press.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
Peter J. Cameron, Sequences realized by oligomorphic permutation groups, J. Int. Seq. 3 (2000), Art. 00.1.5.
M. D. Hendy, C. H. C. Little, and David Penny, Comparing trees with pendant vertices labelled, SIAM J. Appl. Math. 44(5) (1984), 1054-1065. See Table 1.
Max Schwegele, Hyperelliptic Stable Curves, arXiv:2606.29016 [math.AG], 2026. See p. 15.
FORMULA
G.f.: 1+(1+x-B(x))*B(x) where B(x) = x+x^2+2*x^3+5*x^4+12*x^5+33*x^6+90*x^7+... is g.f. for A000669.
MATHEMATICA
(* a9 = A000669 *) max = 29; a9[1] = 1; a9[n_] := (s = Series[1/(1 - x), {x, 0, n}]; Do[s = Series[s/(1 - x^k)^Coefficient[s, x^k], {x, 0, n}], {k, 2, n}]; Coefficient[s, x^n]/2); b[x_] := Sum[a9[n] x^n, {n, 1, max}]; gf[x_] := 1 + (1 + x - b[x])*b[x]; CoefficientList[ Series[gf[x], {x, 0, max}], x] (* Jean-François Alcover, Aug 14 2012 *)
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Matthew Cropper (mmcrop01(AT)athena.louisville.edu)
EXTENSIONS
Corrected and extended by Christian G. Bower, Nov 15 1999
STATUS
approved