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 A030053 a(n) = binomial(2n+1,n-3). 6
 1, 9, 55, 286, 1365, 6188, 27132, 116280, 490314, 2042975, 8436285, 34597290, 141120525, 573166440, 2319959400, 9364199760, 37711260990, 151584480450, 608359048206, 2438362177020, 9762479679106, 39049918716424, 156077261327400, 623404249591760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS Number of UUUUUU's in all Dyck (n+3)-paths. - David Scambler, May 03 2013 LINKS T. D. Noe, Table of n, a(n) for n = 3..200 Milan Janjic, Two Enumerative Functions Asamoah Nkwanta and Earl R. Barnes, Two Catalan-type Riordan Arrays and their Connections to the Chebyshev Polynomials of the First Kind, Journal of Integer Sequences, Article 12.3.3, 2012. - From N. J. A. Sloane, Sep 16 2012. FORMULA G.f.: x^3*128/((1-sqrt(1-4*x))^7*sqrt(1-4*x))+(-1/x^4+5/x^3-6/x^2+1/x). - Vladimir Kruchinin, Aug 11 2015 EXAMPLE G.f. = x^3 + 9*x^4 + 55*x^5 + 286*x^6 + 1365*x^7 + 6188*x68 + ... MAPLE seq((count(Composition(2*n), size=n-3)), n=4..24); # Zerinvary Lajos, May 03 2007 MATHEMATICA Table[Binomial[2*n + 1, n - 3], {n, 3, 20}] (* T. D. Noe, Apr 03 2014 *) Rest[Rest[Rest[CoefficientList[Series[128 x^3 / ((1 - Sqrt[1 - 4 x])^7 Sqrt[1 - 4 x]) + (-1 / x^4 + 5 / x^3 - 6 / x^2 + 1 / x), {x, 0, 40}], x]]]] (* Vincenzo Librandi, Aug 11 2015 *) PROG (PARI) a(n) = binomial(2*n+1, n-3); \\ Joerg Arndt, May 08 2013 (MAGMA) [Binomial(2*n+1, n-3): n in [3..30]]; // Vincenzo Librandi, Aug 11 2015 CROSSREFS Diagonal 8 of triangle A100257. Cf. A113187 (unsigned fourth column). Sequence in context: A263478 A016269 A005770 * A072844 A026857 A244650 Adjacent sequences:  A030050 A030051 A030052 * A030054 A030055 A030056 KEYWORD nonn,easy AUTHOR STATUS approved

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