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 A082958 Number of symmetric short bushes with n edges. 1
 1, 0, 1, 1, 1, 2, 3, 4, 7, 10, 17, 25, 43, 64, 111, 167, 291, 442, 773, 1183, 2075, 3196, 5619, 8702, 15329, 23852, 42085, 65755, 116181, 182186, 322287, 507020, 897859, 1416594, 2510901, 3971887, 7045915, 11171924, 19832947, 31514404, 55982893 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Or number of ordered trees with n edges, no vertices of outdegree 1 and which are symmetrical with respect to the vertical axis passing through the root. LINKS F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999), 73-112. FORMULA G.f.: [(1-z)(1+z^2)-(1+z)sqrt(1-2z^2-3z^4)]/[2z(z^3+z^2+z-1)]. a(n) has antiparity of A007814(n+1), i.e. a(n) mod 2 = A035263(n+1). - Ralf Stephan, Feb 21 2004 CROSSREFS Sequence in context: A136570 A082766 A119016 * A218495 A166012 A060166 Adjacent sequences:  A082955 A082956 A082957 * A082959 A082960 A082961 KEYWORD nonn AUTHOR Emeric Deutsch, May 26 2003 STATUS approved

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Last modified August 3 08:53 EDT 2020. Contains 336197 sequences. (Running on oeis4.)