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 A016758 #31 Sep 08 2022 08:44:41 %S A016758 1,729,15625,117649,531441,1771561,4826809,11390625,24137569,47045881, %T A016758 85766121,148035889,244140625,387420489,594823321,887503681, %U A016758 1291467969,1838265625,2565726409,3518743761,4750104241,6321363049,8303765625,10779215329,13841287201,17596287801 %N A016758 a(n) = (2*n+1)^6. %H A016758 Vincenzo Librandi, <a href="/A016758/b016758.txt">Table of n, a(n) for n = 0..10000</a> %H A016758 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1). %F A016758 a(0)=1, a(1)=729, a(2)=15625, a(3)=117649, a(4)=531441, a(5)=1771561, a(6)=4826809, a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) + 21*a(n-5) -7*a(n-6) +a(n-7). - _Harvey P. Dale_, Dec 26 2012 %F A016758 G.f.: (1 +722*x +10543*x^2 +23548*x^3 +10543*x^4 +722*x^5 +x^6)/(1-x)^7 . - _R. J. Mathar_, Jul 07 2017 %F A016758 Sum_{n>=0} 1/a(n) = Pi^6/960 (A300709). - _Amiram Eldar_, Oct 10 2020 %F A016758 From _Amiram Eldar_, Jan 28 2021: (Start) %F A016758 Product_{n>=0} (1 + 1/a(n)) = cosh(Pi/2)*(cos(sqrt(3)*Pi/2) + cosh(Pi/2))/2. %F A016758 Product_{n>=1} (1 - 1/a(n)) = Pi*cosh(sqrt(3)*Pi/2)/24. (End) %t A016758 (2*Range[0,20]+1)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1, 729,15625,117649,531441,1771561,4826809},20] (* _Harvey P. Dale_, Dec 26 2012 *) %o A016758 (Magma) [(2*n+1)^6: n in [0..30]]; // _Vincenzo Librandi_, Sep 07 2011 %o A016758 (PARI) vector(30, n, n--; (2*n+1)^6) \\ _G. C. Greubel_, Sep 15 2018 %Y A016758 Cf. A300709. %K A016758 nonn,easy %O A016758 0,2 %A A016758 _N. J. A. Sloane_