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 A186231 Expansion of ( 2F1([-1/4, 1/4]; [-1/2], 16*x) - 1 ) / (2*x). 2
 1, 15, 210, 3003, 43758, 646646, 9657700, 145422675, 2203961430, 33578000610, 513791607420, 7890371113950, 121548660036300, 1877405874732108, 29065024282889672, 450883717216034179, 7007092303604022630, 109069992321755544170, 1700179760011004467468, 26536589497469056215210, 414670662257153823494820 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Combinatorial interpretation welcome. Probably a class of paths (Cf. A135404, A000888). Number of North-East lattice paths from (0,0) to (n,n+1). - Michael D. Weiner, Apr 14 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) = A001791(2n+1). - R. J. Mathar, Jul 10 2012 Conjecture: -(n+1)*(2*n-1)*a(n) +2*(4*n-1)*(4*n+1)*a(n-1)=0. - R. J. Mathar, Apr 26 2017 MATHEMATICA CoefficientList[Series[(HypergeometricPFQ[{-(1/4), 1/4}, {-(1/2)}, 16 x] - 1)/(2 x), {x, 0, 20}], x] CROSSREFS Cf. A186229. Sequence in context: A170648 A170696 A170734 * A001880 A240682 A113362 Adjacent sequences:  A186228 A186229 A186230 * A186232 A186233 A186234 KEYWORD nonn AUTHOR Olivier Gérard, Feb 15 2011 STATUS approved

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