This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A069975 #25 Sep 06 2025 00:04:01
%S A069975 15,126,429,1020,1995,3450,5481,8184,11655,15990,21285,27636,35139,
%T A069975 43890,53985,65520,78591,93294,109725,127980,148155,170346,194649,
%U A069975 221160,249975,281190,314901,351204,390195,431970,476625,524256,574959,628830,685965,746460
%N A069975 a(n) = n*(16*n^2 - 1).
%H A069975 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A069975 Sum_{n>=1} 1/a(n) = 3*log(2) - 2 = A016631 - 2. (Ramanujan)
%F A069975 Sum_{n>=1} (-1)^(n+1)/a(n) = 2 - log(2) + sqrt(2)*log(sqrt(2)-1). - _Amiram Eldar_, Jun 24 2022
%F A069975 From _Elmo R. Oliveira_, Sep 05 2025: (Start)
%F A069975 G.f.: 3*x*(5 + 22*x + 5*x^2)/(x-1)^4.
%F A069975 E.g.f.: x*(15 + 48*x + 16*x^2)*exp(x).
%F A069975 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
%F A069975 a(n) = A069140(n)/4. (End)
%t A069975 Table[n(16n^2-1),{n,40}] (* _Harvey P. Dale_, Dec 17 2018 *)
%o A069975 (PARI) a(n) = n*(16*n^2-1); \\ _Michel Marcus_, Nov 25 2013
%o A069975 (PARI) my(x='x+O('x^37)); Vec(3*x*(5+22*x+5*x^2)/(1-x)^4) \\ _Elmo R. Oliveira_, Sep 05 2025
%Y A069975 Cf. A016631, A069140.
%K A069975 easy,nonn,changed
%O A069975 1,1
%A A069975 _Benoit Cloitre_, Apr 30 2002
%E A069975 More terms from _Elmo R. Oliveira_, Sep 05 2025