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 A152744 #36 Feb 27 2022 05:46:30
%S A152744 0,7,35,84,154,245,357,490,644,819,1015,1232,1470,1729,2009,2310,2632,
%T A152744 2975,3339,3724,4130,4557,5005,5474,5964,6475,7007,7560,8134,8729,
%U A152744 9345,9982,10640,11319,12019,12740,13482,14245,15029,15834,16660,17507,18375,19264
%N A152744 7 times pentagonal numbers: a(n) = 7*n*(3*n-1)/2.
%H A152744 Ivan Panchenko, <a href="/A152744/b152744.txt">Table of n, a(n) for n = 0..1000</a>
%H A152744 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152744 a(n) = (21*n^2 - 7*n)/2 = A000326(n)*7.
%F A152744 a(n) = a(n-1) + 21*n - 14 (with a(0)=0). - _Vincenzo Librandi_, Nov 26 2010
%F A152744 G.f.: 7*x*(1+2*x)/(1-x)^3. - _Colin Barker_, Feb 14 2012
%F A152744 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - _Harvey P. Dale_, Aug 08 2013
%F A152744 a(n) = Sum_{i = 2..8} P(i,n), where P(i,m) = m*((i-2)*m-(i-4))/2. - _Bruno Berselli_, Jul 04 2018
%F A152744 E.g.f.: 7*x*(2+3*x)/2. - _G. C. Greubel_, Sep 01 2018
%F A152744 From _Amiram Eldar_, Feb 27 2022: (Start)
%F A152744 Sum_{n>=1} 1/a(n) = (9*log(3) - sqrt(3)*Pi)/21.
%F A152744 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(Pi*sqrt(3) - 6*log(2))/21. (End)
%t A152744 Table[7n (3n-1)/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,7,35},50] (* _Harvey P. Dale_, Aug 08 2013 *)
%o A152744 (PARI) a(n)=7*n*(3*n-1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A152744 (Magma) [7*n*(3*n-1)/2: n in [0..50]]; // _G. C. Greubel_, Sep 01 2018
%Y A152744 Cf. A000326, A014642, A152743.
%Y A152744 Similar sequences are listed in A316466.
%K A152744 nonn,easy
%O A152744 0,2
%A A152744 _Omar E. Pol_, Dec 12 2008