A173121 a(n) = sinh(2*arccosh(n))^2 = 4*n^2*(n^2 - 1).

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

Offset: 0

Author

Artur Jasinski, Feb 10 2010

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A002415, A047928, A001079, A037270, A071253, A108741, A132592, A146311-A146313, A173115.

Programs

Magma

[4*n^2*(n^2-1): n in [0..40]]; // Vincenzo Librandi, Jun 15 2011

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 *)

PARI

a(n)=4*n^2*(n^2-1) \\ Charles R Greathouse IV, Jul 01 2013

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)