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 A228343 The number of ordered trees with bicolored single edges on the boundary. 0
 1, 2, 5, 15, 50, 175, 625, 2251, 8142, 29544, 107538, 392726, 1439204, 5292833, 19533241, 72333107, 268728214, 1001448308, 3742866166, 14026901282, 52701685564, 198481560878, 749170991770, 2833635556670, 10738689128460, 40770816357920, 155056284790340, 590644481896972 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES D. E. Davenport, L. K. Pudwell, L. W. Shapiro, L. C. Woodson, The Boundary of Ordered Trees, 2014; http://faculty.valpo.edu/lpudwell/papers/treeboundary.pdf LINKS Dennis E. Davenport, Lara K. Pudwell, Louis W. Shapiro, Leon C. Woodson, The Boundary of Ordered Trees, Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.8. FORMULA G.f.: (1+x^2*C^5)/(1-2*x) where C is the Catalan number generating function (cf. A000108). Conjecture: -(n+3)*(n-2)*a(n) +6*(n^2-2)*a(n-1) -4*n*(2*n-1)*a(n-2)=0. - R. J. Mathar, Aug 25 2013 a(n) -2*a(n-1) = A000344(n). - R. J. Mathar, Aug 25 2013 a(n) ~ 5 * 2^(2*n+1) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Jan 31 2014 EXAMPLE When n=3 the five trees contribute as follows: UUUDDD 8; UUDDUD, UDUUDD,UUDUDD 2 each; and UDUDUD just 1. MATHEMATICA Table[FullSimplify[I*2^n - 5/2*Gamma[3+2*n] * HypergeometricPFQRegularized[{1, 3/2+n, 2+n}, {n, 5+n}, 2]], {n, 0, 20}] (* Vaclav Kotesovec, Jan 31 2014 *) PROG (PARI) x = 'x + O('x^66); C = serreverse( x/( 1/(1-x) ) ) / x; \\ Catalan A000108 gf = (1+x^2*C^5)/(1-2*x); Vec(gf) \\ Joerg Arndt, Aug 21 2013 CROSSREFS Cf. A000108, A228197. Sequence in context: A149948 A093129 A020876 * A149949 A149950 A024718 Adjacent sequences:  A228340 A228341 A228342 * A228344 A228345 A228346 KEYWORD nonn AUTHOR Louis Shapiro, Aug 20 2013 STATUS approved

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Last modified May 24 11:23 EDT 2019. Contains 323529 sequences. (Running on oeis4.)