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 A300126 Number of Motzkin trees that are "uniquely closable skeletons". 2
 0, 1, 0, 1, 1, 2, 2, 7, 5, 20, 19, 60, 62, 202, 202, 679, 711, 2304, 2507, 8046, 8856, 28434, 31855, 101288, 115596, 364710, 421654, 1323946, 1549090, 4836072, 5724582, 17771683, 21250527, 65653884, 79227989, 243639954, 296543356, 907841678, 1113706887 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS From the Bodini-Tarau paper: "Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices". For the relation to the set of Motzkin trees where all leaves are at the same unary height see A321396. - Peter Luschny, Nov 14 2018 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Olivier Bodini, Paul Tarau, On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms, arXiv:1709.04302 [cs.PL], 2017. FORMULA G.f.: -(sqrt(2*z*(sqrt(1 - 4*z^2) - 1) + 1) - 1)/(2*z^2). - Peter Luschny, Nov 14 2018 MAPLE gf := -(sqrt(2*z*(sqrt(1 - 4*z^2) - 1) + 1) - 1)/(2*z^2): series(gf, z, 44): seq(coeff(%, z, n), n=0..38); # Peter Luschny, Nov 14 2018 MATHEMATICA CoefficientList[Series[(1-Sqrt[1 + 2*x*(Sqrt[1-4*x^2]-1)])/(2*x^2), {x, 0, 50}], x] (* G. C. Greubel, Nov 14 2018 *) PROG (PARI) x='x+O('x^50); concat([0], Vec((1-sqrt(1 + 2*x*(sqrt(1-4*x^2) -1)))/(2*x^2))) \\ G. C. Greubel, Nov 14 2018 (MAGMA) m:=50; R:=PowerSeriesRing(Rationals(), m); [0] cat Coefficients(R!( (1-Sqrt(1 + 2*x*(Sqrt(1-4*x^2) -1)))/(2*x^2) )); // G. C. Greubel, Nov 14 2018 (Sage) s= (-(sqrt(2*x*(sqrt(1 - 4*x^2) - 1) + 1) - 1)/(2*x^2)).series(x, 30); s.coefficients(x, sparse=False) # G. C. Greubel, Nov 14 2018 CROSSREFS Cf. A000108, A001006, A135501, A321396 (row 1). Sequence in context: A249493 A223000 A058625 * A006748 A193548 A131049 Adjacent sequences:  A300123 A300124 A300125 * A300127 A300128 A300129 KEYWORD nonn AUTHOR Michael De Vlieger, Feb 25 2018 STATUS approved

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Last modified February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)