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 A101308 Number of ordered trees with n edges and having no branches of length 2. 1
 1, 1, 1, 3, 7, 18, 47, 129, 362, 1038, 3022, 8917, 26600, 80098, 243132, 743180, 2285597, 7067271, 21957947, 68517606, 214633572, 674712991, 2127790260, 6729876378, 21342679122, 67851885121, 216204228642, 690371596017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Column 0 of the triangle A101307. REFERENCES E. Deutsch, Ordered trees with prescribed root degrees, node degrees and branch lengths, Discrete Math., 282, 2004, 89-94. J. Riordan, Enumeration of plane trees by branches and endpoints, J. Comb. Theory (A) 19, 1975, 214-222. LINKS FORMULA G.f.=[1-z^2+z^3-sqrt[(1-z^2+z^3)(1-4z+3z^2-3z^3)]]/[2z(1-z+z^2)]. EXAMPLE a(3)=3 because we have:(i) a path of length tree hanging from the root, (ii) an edge hanging from the root, from the end of which two edges are hanging and (iii) three edges hanging from the root. MAPLE G:=(1-z^2+z^3-sqrt((1-z^2+z^3)*(1-4*z+3*z^2-3*z^3)))/2/z/(1-z+z^2): Gser:=series(G, z=0, 34): 1, seq(coeff(Gser, z^n), n=1..32); CROSSREFS Cf. A101307. Sequence in context: A211276 A018028 A045994 * A018029 A099483 A225034 Adjacent sequences:  A101305 A101306 A101307 * A101309 A101310 A101311 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 22 2004 STATUS approved

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