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 A069071 #28 Sep 03 2025 13:54:29
%S A069071 5,255,3145,16835,59085,161095,371345,759435,1419925,2476175,4084185,
%T A069071 6436435,9765725,14349015,20511265,28629275,39135525,52522015,
%U A069071 69344105,90224355,115856365,147008615,184528305,229345195,282475445,345025455,418195705,503284595,601692285
%N A069071 a(n) = (2*n + 1)*((2*n + 1)^4 + 4).
%C A069071 The formula for Pi in the formula section was discovered by the mathematician and astronomer Nilakantha Somayaji (1444-1544) (Roy, 1990). - _Amiram Eldar_, Jan 18 2023
%H A069071 Amiram Eldar, <a href="/A069071/b069071.txt">Table of n, a(n) for n = 0..10000</a>
%H A069071 Ranjan Roy, <a href="https://www.jstor.org/stable/2690896">The Discovery of the Series Formula for Pi by Leibniz, Gregory and Nilakantha</a>, Mathematics Magazine, Vol. 63, No. 5 (Dec., 1990), pp. 291-306.
%H A069071 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A069071 Pi = 16 * Sum_{n>=0} (-1)^n/a(n).
%F A069071 From _Elmo R. Oliveira_, Sep 03 2025: (Start)
%F A069071 G.f.: 5*(1 + x)*(1 + 44*x + 294*x^2 + 44*x^3 + x^4)/(x-1)^6.
%F A069071 E.g.f.: (5 + 250*x + 1320*x^2 + 1360*x^3 + 400*x^4 + 32*x^5)*exp(x).
%F A069071 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). (End)
%t A069071 a[n_] := (2*n + 1)*((2*n + 1)^4 + 4); Array[a, 30, 0] (* _Amiram Eldar_, Jul 16 2022 *)
%Y A069071 Cf. A019683.
%K A069071 easy,nonn,changed
%O A069071 0,1
%A A069071 _Benoit Cloitre_, Apr 05 2002