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 A266565 #19 Mar 27 2024 20:11:29 %S A266565 9,2,9,8,4,0,4,1,1,8,2,2,9,4,0,0,8,8,0,4,3,1,1,3,7,8,5,0,3,7,6,0,4,3, %T A266565 3,4,4,4,5,3,5,3,8,1,5,9,6,6,5,5,8,4,8,9,9,7,9,3,6,1,1,4,8,0,2,9,7,2, %U A266565 4,8,3,6,0,3,6,8,0,0,5,9,0,5,2,0,6,1,7,1,9,7,2,1,4 %N A266565 Decimal expansion of the generalized Glaisher-Kinkelin constant A(18). %C A266565 Also known as the 18th Bendersky constant. %H A266565 G. C. Greubel, <a href="/A266565/b266565.txt">Table of n, a(n) for n = 6..2007</a> %F A266565 A(k) = exp(H(k)*B(k+1)/(k+1) - zeta'(-k)), where B(k) is the k-th Bernoulli number, H(k) the k-th harmonic number, and zeta'(x) is the derivative of the Riemann zeta function. %F A266565 A(18) = exp((B(18)/4)*(zeta(19)/zeta(18))) = exp(-zeta'(-18)). %F A266565 A(18) = exp(18! * Zeta(19) / (2^19 * Pi^18)). - _Vaclav Kotesovec_, Jan 01 2016 %e A266565 929840.411822940088043113785037604334445353815966558489979361... %t A266565 Exp[N[(BernoulliB[18]/4)*(Zeta[19]/Zeta[18]), 200]] %Y A266565 Cf. A019727 (A(0)), A074962 (A(1)), A243262 (A(2)), A243263 (A(3)), A243264 (A(4)), A243265 (A(5)), A266553 (A(6)), A266554 (A(7)), A266555 (A(8)), A266556 (A(9)), A266557 (A(10)), A266558 (A(11)), A266559 (A(12)), A260662 (A(13)), A266560 (A(14)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266566 (A(19)), A266567 (A(20)). %Y A266565 Cf. A013676, A013677, A266273, A027641, A027642. %K A266565 nonn,cons %O A266565 6,1 %A A266565 _G. C. Greubel_, Dec 31 2015