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 A266564 #28 Mar 06 2025 04:44:28
%S A266564 1,5,9,6,5,3,5,0,8,5,7,5,8,0,3,8,5,5,3,8,5,1,4,5,5,2,3,6,6,2,0,4,4,1,
%T A266564 9,4,5,3,3,1,6,6,1,1,0,0,6,1,3,5,0,4,4,4,3,4,1,4,5,5,4,6,3,9,9,9,7,1,
%U A266564 1,0,6,0,4,5,3,4,3,2,2,9,5,6,3,5,0,6,5,4,0,4,2,1,1
%N A266564 Decimal expansion of the generalized Glaisher-Kinkelin constant A(17).
%C A266564 Also known as the 17th Bendersky constant.
%H A266564 G. C. Greubel, <a href="/A266564/b266564.txt">Table of n, a(n) for n = 4..2003</a>
%H A266564 Victor S. Adamchik, <a href="https://doi.org/10.1016/S0377-0427(98)00192-7">Polygamma functions of negative order</a>, Journal of Computational and Applied Mathematics, Vol. 100, No. 2 (1998), pp. 191-199.
%H A266564 L. Bendersky, <a href="https://doi.org/10.1007/BF02547794">Sur la fonction gamma généralisée</a>, Acta Mathematica , Vol. 61 (1933), pp. 263-322; <a href="https://projecteuclid.org/journals/acta-mathematica/volume-61/issue-none/Sur-la-fonction-gamma-g%C3%A9n%C3%A9ralis%C3%A9e/10.1007/BF02547794.full">alternative link</a>.
%H A266564 Robert A. Van Gorder, <a href="https://doi.org/10.1142/S1793042112500297">Glaisher-type products over the primes</a>, International Journal of Number Theory, Vol. 8, No. 2 (2012), pp. 543-550.
%H A266564 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.
%F A266564 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 A266564 A(17) = exp(H(17)*B(18)/18 - zeta'(-17)) = exp((B(18)/18)*(EulerGamma + log(2*Pi) - zeta'(18)/zeta(18))).
%F A266564 Equals (2*Pi*exp(gamma) * Product_{p prime} p^(1/(p^18-1)))^c, where gamma is Euler's constant (A001620), and c = Bernoulli(18)/18 = 43867/14364 (Van Gorder, 2012). - _Amiram Eldar_, Feb 08 2024
%e A266564 1596.53508575803855385145523662044194533166110061350444341....
%t A266564 Exp[N[(BernoulliB[18]/18)*(EulerGamma + Log[2*Pi] - Zeta'[18]/Zeta[18]), 200]]
%Y A266564 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)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).
%Y A266564 Cf. A001620, A013676, A266272, A027641, A027642, A001008, A002805.
%K A266564 nonn,cons
%O A266564 4,2
%A A266564 _G. C. Greubel_, Dec 31 2015