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A167713
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a(n) = 16^n * Sum_{k=0..n} binomial(2*k, k) / 16^k.
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8
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1, 18, 294, 4724, 75654, 1210716, 19372380, 309961512, 4959397062, 79350401612, 1269606610548, 20313706474200, 325019306291356, 5200308911062296, 83204942617113336, 1331279082028930896, 21300465313063974726
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OFFSET
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0,2
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COMMENTS
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p^2 divides a((p-3)/2) for prime p of the form p = 6k + 1 (A002476).
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LINKS
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FORMULA
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a(n) = 16^n * Sum_{k=0..n} ((2k)!/(k!)^2) / 16^k.
a(n) = 16^n * Sum_{k=0..n} binomial(2k,k) / 16^k.
Recurrence: n*a(n) = 2*(10*n-1)*a(n-1) - 32*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 20 2012
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MAPLE
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MATHEMATICA
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16^n * Sum[ (2k)!/(k!)^2 / 16^k, {k, 0, 50} ].
CoefficientList[Series[1 / ((1 - 16 x) Sqrt[1 - 4 x]), {x, 0, 20}], x] (* Vincenzo Librandi, May 27 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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