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 A196506 #23 Sep 08 2022 08:45:59 %S A196506 0,15,120,435,1128,2415,4560,7875,12720,19503,28680,40755,56280,75855, %T A196506 100128,129795,165600,208335,258840,318003,386760,466095,557040, %U A196506 660675,778128,910575,1059240,1225395,1410360,1615503,1842240,2092035 %N A196506 a(n) = 1*3*5 + 3*5*7 + 5*7*9 + ... (n terms). %C A196506 All terms are multiples of 3. %D A196506 Jolley, Summation of Series, Dover (1961), eq (43) page 8. %H A196506 Vincenzo Librandi, <a href="/A196506/b196506.txt">Table of n, a(n) for n = 0..10000</a> %H A196506 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A196506 a(n) = ((4n^2 - 1)*(2n + 3)*(2n + 5) + 15)/ 8 = Sum_{i=1..n} (2i - 1)*(2i + 1)*(2i + 3). %F A196506 G.f. -3*x*(5 + 15*x - 5*x^2 + x^3) / (x-1)^5 . %F A196506 a(n) = 2 n^4 + 8 n^3 + 7 n^2 - 2 n. - _Harvey P. Dale_, Mar 14 2015, corrected by _Eric Rowland_, Aug 15 2017 %t A196506 LinearRecurrence[{5,-10,10,-5,1},{0,15,120,435,1128},40] (* or *) Accumulate[ Join[{0},Times@@@Partition[Range[1,111,2],3,1]]] (* or *) Table[2n^4-5n^2+3,{n,40}](* _Harvey P. Dale_, Mar 14 2015 *) %o A196506 (Magma) [((4*n^2-1)*(2*n+3)*(2*n+5)+15)/ 8 : n in [0..30]]; // _Vincenzo Librandi_, Oct 05 2011 %Y A196506 Cf. A061550 (first differences). %K A196506 nonn,easy %O A196506 0,2 %A A196506 _R. J. Mathar_, Oct 03 2011