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A267796
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a(n) = (n+1)*4^(2n+1).
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4
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4, 128, 3072, 65536, 1310720, 25165824, 469762048, 8589934592, 154618822656, 2748779069440, 48378511622144, 844424930131968, 14636698788954112, 252201579132747776, 4323455642275676160, 73786976294838206464, 1254378597012249509888, 21250649172913403461632
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OFFSET
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0,1
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COMMENTS
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The partial sums of A001246(n)/a(n) converge absolutely. This series is also the hypergeometric function 1/4 * 4F3(1/2,1/2,1,1;2,2,2;1). - Ralf Steiner, Feb 09 2016
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LINKS
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FORMULA
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G.f.: 4 / (1 - 16*x)^2.
a(n) = 32*a(n-1) - 256*a(n-2) for n>1. (End)
Sum_{n>=0} 1/a(n) = 4*log(16/15).
Sum_{n>=0} (-1)^n/a(n) = 4*log(17/16). (End)
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EXAMPLE
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For n=3, a(3) = (3+1)*4^(2*3+1) = 4*4^7 = 65536.
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MATHEMATICA
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PROG
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(PARI) Vec(4 / (1 - 16*x)^2 + O(x^30)) \\ Colin Barker, Mar 23 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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