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A173121
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a(n) = sinh(2*arccosh(n))^2 = 4*n^2*(n^2 - 1).
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21
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0, 0, 48, 288, 960, 2400, 5040, 9408, 16128, 25920, 39600, 58080, 82368, 113568, 152880, 201600, 261120, 332928, 418608, 519840, 638400, 776160, 935088, 1117248, 1324800, 1560000, 1825200, 2122848, 2455488, 2825760, 3236400, 3690240
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = 48*A002415(n) = 4*A047928(n).
G.f.: 48*x^2*(1+x)/(1-x)^5. - Colin Barker, Mar 22 2012
From Amiram Eldar, Jul 26 2022: (Start)
Sum_{n>=2} 1/a(n) = (21 - 2*Pi^2)/48.
Sum_{n>=2} (-1)^n/a(n) = (Pi^2 - 9)/48. (End)
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MATHEMATICA
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Table[4 n^2*(n^2 - 1), {n, 0, 30}] (* or *) Table[Round[N[Sinh[2 ArcCosh[n]]^2, 100]], {n, 0, 50}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 48, 288, 960}, 40] (* Harvey P. Dale, Jul 22 2015 *)
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PROG
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(Magma) [4*n^2*(n^2-1): n in [0..40]]; // Vincenzo Librandi, Jun 15 2011
(PARI) a(n)=4*n^2*(n^2-1) \\ Charles R Greathouse IV, Jul 01 2013
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CROSSREFS
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Cf. A002415, A047928, A001079, A037270, A071253, A108741, A132592, A146311-A146313, A173115.
Sequence in context: A001337 A259993 A205747 * A281234 A215262 A097639
Adjacent sequences: A173118 A173119 A173120 * A173122 A173123 A173124
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KEYWORD
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nonn,easy
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AUTHOR
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Artur Jasinski, Feb 10 2010
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STATUS
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approved
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