login
a(n) = n*(16*n^2-1).
0

%I #21 Jun 24 2022 04:34:04

%S 15,126,429,1020,1995,3450,5481,8184,11655,15990,21285,27636,35139,

%T 43890,53985,65520,78591,93294,109725,127980,148155,170346,194649,

%U 221160,249975,281190,314901,351204,390195,431970,476625,524256,574959

%N a(n) = n*(16*n^2-1).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F Sum_{n>=1} 1/a(n) = 3*log(2) - 2 = A016631 - 2. (Ramanujan)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2 - log(2) + sqrt(2)*log(sqrt(2)-1). - _Amiram Eldar_, Jun 24 2022

%t Table[n(16n^2-1),{n,40}] (* _Harvey P. Dale_, Dec 17 2018 *)

%o (PARI) a(n) = n*(16*n^2-1); \\ _Michel Marcus_, Nov 25 2013

%Y Cf. A016631.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Apr 30 2002