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 A266562 #29 Mar 06 2025 04:44:34
%S A266562 3,4,2,8,3,0,8,0,6,1,3,2,8,1,6,7,3,6,5,7,1,7,1,1,1,4,6,3,4,0,6,7,2,3,
%T A266562 7,8,1,4,1,7,2,6,9,4,5,4,8,3,2,3,6,8,7,7,2,5,1,0,7,6,1,6,4,2,4,1,9,2,
%U A266562 6,5,5,3,5,8,7,9,7,1,1,2,8,5,2,1,3,8,4,9,6,0,2,5,9,3
%N A266562 Decimal expansion of the generalized Glaisher-Kinkelin constant A(15).
%C A266562 Also known as the 15th Bendersky constant.
%H A266562 G. C. Greubel, <a href="/A266562/b266562.txt">Table of n, a(n) for n = 0..2000</a>
%H A266562 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 A266562 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 A266562 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 A266562 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.
%F A266562 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 A266562 A(15) = exp(H(15)*B(16)/16 - zeta'(-15)) = exp((B(16)/16)*(EulerGamma + log(2*Pi) - zeta'(16)/zeta(16))).
%F A266562 Equals (2*Pi*exp(gamma) * Product_{p prime} p^(1/(p^16-1)))^c, where gamma is Euler's constant (A001620), and c = Bernoulli(16)/16 = -3617/8160 (Van Gorder, 2012). - _Amiram Eldar_, Feb 08 2024
%e A266562 0.342830806132816736571711146340672378141726945483236877251076164....
%t A266562 Exp[N[(BernoulliB[16]/16)*(EulerGamma + Log[2*Pi] - Zeta'[16]/Zeta[16]), 200]]
%Y A266562 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)), A266563 (A(16)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).
%Y A266562 Cf. A001620, A013674, A266270, A027641, A027642, A001008, A002805.
%K A266562 nonn,cons
%O A266562 0,1
%A A266562 _G. C. Greubel_, Dec 31 2015