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 A173308 #37 Dec 15 2024 09:30:45
%S A173308 0,34,102,204,340,510,714,952,1224,1530,1870,2244,2652,3094,3570,4080,
%T A173308 4624,5202,5814,6460,7140,7854,8602,9384,10200,11050,11934,12852,
%U A173308 13804,14790,15810,16864,17952,19074,20230,21420,22644,23902,25194,26520,27880,29274,30702
%N A173308 a(n) = 17*n*(n+1).
%H A173308 Vincenzo Librandi, <a href="/A173308/b173308.txt">Table of n, a(n) for n = 0..1000</a>
%H A173308 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A173308 a(n) = 34*A000217(n).
%F A173308 From _Colin Barker_, Jan 25 2012: (Start)
%F A173308 a(0)=0, a(1)=34, a(2)=102, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A173308 G.f.: 34*x/(1-x)^3. (End)
%F A173308 From _Amiram Eldar_, Feb 22 2023: (Start)
%F A173308 Sum_{n>=1} 1/a(n) = 1/17.
%F A173308 Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/17.
%F A173308 Product_{n>=1} (1 - 1/a(n)) = -(17/Pi)*cos(sqrt(21/17)*Pi/2).
%F A173308 Product_{n>=1} (1 + 1/a(n)) = (17/Pi)*cos(sqrt(13/17)*Pi/2). (End)
%F A173308 From _Elmo R. Oliveira_, Dec 14 2024: (Start)
%F A173308 E.g.f.: 17*exp(x)*x*(2 + x).
%F A173308 a(n) = 17*A002378(n) = 2*A195037(n). (End)
%t A173308 Table[17n(n+1),{n,0,40}] (* _Harvey P. Dale_, Apr 06 2011 *)
%o A173308 (PARI) a(n)=34*binomial(n+1,2) \\ _Charles R Greathouse IV_, Jan 25 2012
%o A173308 (Magma) [17*n*(n+1): n in [0..50]]; // _Vincenzo Librandi_, Aug 20 2014
%Y A173308 Cf. A000217, A002378, A195037.
%K A173308 nonn,easy
%O A173308 0,2
%A A173308 _Vincenzo Librandi_, Feb 16 2010
%E A173308 Incorrect formulas and examples deleted by _R. J. Mathar_, Jan 04 2011