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 A242600 #22 Nov 09 2024 07:48:57
%S A242600 5,4,2,1,9,1,2,1,6,4,5,0,6,9,3,3,7,8,3,4,0,5,0,1,5,3,1,0,4,2,6,4,3,6,
%T A242600 9,5,6,7,9,3,7,6,7,8,5,4,5,8,0,6,9,9,3,9,6,8,6,5,7,2,6,7,7,4,0,3,1,0,
%U A242600 5,3,1,5,3,7,7,7,9,9,4,4,3,0,4,0,9,2,4,2,8,6,7,0,4,7,0,9,2,8,4,5,9,3,7,3,0,1,3
%N A242600 Decimal expansion of -dilog(phi) = -polylog(2, 1-phi) with phi = (1 + sqrt(5))/2.
%C A242600 This solution for -Sum_{k>=1} (-2*sin(Pi/10)^k/k^2) should also have been mentioned in the Jolley reference pp. 66-69 under (360).
%D A242600 L. B. W. Jolley, Summation of Series, Dover, 1961.
%H A242600 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%F A242600 Equals -Sum_{k>=1} (1-phi)^k/k^2 = Pi^2/15 - (log(phi-1)^2)/2, with the golden section phi = (1 + sqrt(5))/2. See the Abramowitz-Stegun link, p. 1004, eqs. 27.7.3 - 27.7.6 with x = phi-1, solving for -dilog(x+1) = -f(1+x), using log(2-phi) = 2*log(phi-1).
%e A242600 0.542191216450693...
%t A242600 RealDigits[PolyLog[2, 1 - GoldenRatio], 10, 120][[1]] (* _Amiram Eldar_, May 30 2023 *)
%Y A242600 Cf. A001622, A076788 (polylog(2,1/2)), A152115, A242599.
%K A242600 nonn,cons
%O A242600 1,1
%A A242600 _Wolfdieter Lang_, Jun 16 2014