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 A268329 Expansion of (1 - sqrt(1 - 4*x))^5/16. 0
 2, 10, 40, 150, 550, 2002, 7280, 26520, 96900, 355300, 1307504, 4828850, 17895150, 66533250, 248124000, 927983760, 3479939100, 13082337900, 49295766000, 186156379500, 704415740028, 2670587146260, 10142836030240, 38586876202000, 147029304149000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 COMMENTS a(n) is the number of North-East paths from (0,0) to (n,n) that cross the diagonal vertically exactly once and horizontally exactly twice, and bounce off the diagonal to the right once but not to the left. Details about this sequence can be found in Section 4.5 in Pan and Remmel's link. - Ran Pan, Feb 01 2016 LINKS Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016. FORMULA G.f.: (1 - sqrt(1 - 4*x))^5/16. a(n) = 10 * binomial(2n-6,n-5)/n. a(n) = 2*A000344(n-3). - R. J. Mathar, Feb 17 2016 n*(n-5)*a(n) -2*(n-3)*(2*n-7)*a(n-1)=0. - R. J. Mathar, Feb 17 2016 MATHEMATICA Table[10 Binomial[2 n - 6, n - 5]/n, {n, 5, 29}] (* or *) Table[SeriesCoefficient[(1 - Sqrt[1 - 4 x])^5/16, {x, 0, n}], {n, 5, 29}] (* Michael De Vlieger, Feb 17 2016 *) CROSSREFS Cf. A000344, A000984. Sequence in context: A174395 A320526 A193519 * A223095 A052978 A151023 Adjacent sequences:  A268326 A268327 A268328 * A268330 A268331 A268332 KEYWORD nonn AUTHOR Ran Pan, Feb 01 2016 STATUS approved

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Last modified October 13 19:48 EDT 2019. Contains 327981 sequences. (Running on oeis4.)