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 A173121 a(n) = sinh(2*arccosh(n))^2 = 4*n^2*(n^2 - 1). 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS 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). FORMULA 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) MATHEMATICA 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 *) PROG (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 CROSSREFS 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 KEYWORD nonn,easy AUTHOR Artur Jasinski, Feb 10 2010 STATUS approved

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)