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A185247
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Expansion of 3F2( (1/4,1/2,3/4); (4,6) )(256 x)
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1
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1, 1, 12, 330, 14300, 831402, 59491432, 4971783960, 468842704200, 48707547603000, 5478624954385440, 658555622357831640, 83752779737507765040, 11180459218164097480500, 1556759031871924444410000, 224927463853886185614776400, 33579302695870956078753329400, 5161336349665341660810732336600
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OFFSET
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0,3
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COMMENTS
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Combinatorial interpretation welcome.
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LINKS
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FORMULA
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D-finite with recurrence n*(n+5)*(n+3)*a(n) -8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022
a(n) = 720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!).
a(n) ~ 45 * 2^(8*n + 7/2) / (Pi^(3/2) * n^(19/2)). (End)
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MATHEMATICA
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CoefficientList[Series[HypergeometricPFQ[{1/4, 1/2, 3/4}, {4, 6}, 256 x], {x, 0, 20}], x]
Table[720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!), {n, 0, 20}] (* Vaclav Kotesovec, Feb 17 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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