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A186229
Expansion of (2F1( (-(1/2), 1/6); (-2/3))( 16 x) -1)/(2*x).
2
1, 14, 182, 2470, 34580, 494760, 7191690, 105793545, 1570873850, 23500272796, 353724885332, 5351515200668, 81313973049064, 1240116577389200, 18973783634054760, 291115203548084370, 4477664537437798980, 69023046543088792440, 1066084706728274263800, 16495237916832025427160, 255635559046076610807120
OFFSET
0,2
COMMENTS
Combinatorial interpretation welcome.
Probably a class of paths (Cf. A135404, A000888)
LINKS
FORMULA
D-finite with recurrence (n+1)*(3n-2)*a(n) = 4*(6n+1)*(2n-1)*a(n-1). - R. J. Mathar, Jul 11 2012
a(n) ~ 3*GAMMA(2/3)*2^(1/3) * 16^n/(Pi*n^(2/3)). - Vaclav Kotesovec, Aug 13 2013
a(n) = -2^(1/3+4*n)*(-4/3)!*(-1/2+n)!*(1/6+n)!/(Pi*(-2/3+n)!*(1+n)!). - Benedict W. J. Irwin, Jul 12 2016
MATHEMATICA
CoefficientList[Series[(HypergeometricPFQ[{-(1/2), 1/6}, {-(2/3)}, 16 x] - 1)/(2 x), {x, 0, 20}], x]
FullSimplify[Table[-((2^(1/3 + 4 n) (-(4/3))! (-(1/2) + n)! (1/6 + n)!)/(Pi (-(2/3) + n)! (1 + n)!)), {n, 0, 20}]] (* Benedict W. J. Irwin, Jul 12 2016 *)
CROSSREFS
Sequence in context: A170647 A170695 A170733 * A181237 A091030 A179090
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Feb 15 2011
STATUS
approved