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
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
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Feb 10 2010
STATUS
approved