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 A111144 #31 Jul 30 2024 04:26:54
%S A111144 0,35,80,136,204,285,380,490,616,759,920,1100,1300,1521,1764,2030,
%T A111144 2320,2635,2976,3344,3740,4165,4620,5106,5624,6175,6760,7380,8036,
%U A111144 8729,9460,10230,11040,11891,12784,13720,14700,15725,16796,17914,19080,20295,21560
%N A111144 a(n) = n*(n+13)*(n+14)/6.
%C A111144 After a(1) all values have at least three prime factors with multiplicity, for example a(33) = 11891 = 11 * 23 * 47 and a(49) = 31899 = 3 * 7^3 * 31.
%H A111144 Vincenzo Librandi, <a href="/A111144/b111144.txt">Table of n, a(n) for n = 0..10000</a>
%H A111144 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A111144 a(n) = A000292(n) + 4n^2 + 30n.
%F A111144 G.f.: x*(35 - 60*x + 26*x^2)/(1-x)^4. - _Colin Barker_, Jan 11 2012
%F A111144 From _Amiram Eldar_, Jul 30 2024: (Start)
%F A111144 Sum_{n>=1} 1/a(n) = 811373/65585520.
%F A111144 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/13 - 752153/7287280. (End)
%t A111144 Table[n (n + 13) (n + 14)/6, {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 06 2011 *)
%o A111144 (Magma) [n*(n+13)*(n+14)/6: n in [0..50]]; // _Vincenzo Librandi_, Jan 11 2012
%o A111144 (PARI) a(n)=n*(n+13)*(n+14)/6 \\ _Charles R Greathouse IV_, Jan 11 2012
%Y A111144 Cf. A000292, A111396.
%K A111144 easy,nonn
%O A111144 0,2
%A A111144 _Jonathan Vos Post_, Nov 12 2005