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 A260662 #43 Feb 16 2025 08:33:26
%S A260662 1,2,2,2,9,4,4,2,5,1,8,0,8,1,3,3,8,7,2,6,4,7,8,9,9,9,6,0,7,2,7,7,1,7,
%T A260662 9,8,8,5,6,1,2,6,5,8,0,3,1,2,9,5,3,2,9,5,0,1,0,8,3,7,2,8,1,0,3,4,4,6,
%U A260662 0,6,4,2,2,7,6,8,6,6,2,0,3,0,3,0,0,1,2,6,4,2,6,9,2,1,7,5,1,1,4,2,6,1,2,4,4,9,1,8,3,6,0,0,2,0,9
%N A260662 Decimal expansion of the generalized Glaisher-Kinkelin constant A(13).
%C A260662 Also known as the thirteenth Bendersky constant.
%H A260662 G. C. Greubel, <a href="/A260662/b260662.txt">Table of n, a(n) for n = 1..2001</a>
%H A260662 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 A260662 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 A260662 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 A260662 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.
%F A260662 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 A260662 A(13) = exp((1/14)*HarmonicNumber(13)*Bernoulli(14) - RiemannZeta'(-13)).
%F A260662 A(13) = exp((B(14)/14)*(EulerGamma + Log(2*Pi) - (zeta'(14)/zeta(14)))).
%F A260662 Equals (2*Pi*exp(gamma) * Product_{p prime} p^(1/(p^14-1)))^c, where gamma is Euler's constant (A001620), and c = Bernoulli(14)/14 = 1/12 (Van Gorder, 2012). - _Amiram Eldar_, Feb 08 2024
%e A260662 1.2229442518081338726478999607277179885...
%t A260662 N[Exp[(1/14)*HarmonicNumber[13]*BernoulliB[14] - Zeta'[-13]], 100]
%t A260662 Exp[N[(BernoulliB[14]/14)*(EulerGamma + Log[2*Pi] - Zeta'[14]/Zeta[14]), 200]]
%Y A260662 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)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).
%Y A260662 Cf. A001620, A260660, A260663.
%K A260662 nonn,cons,easy
%O A260662 1,2
%A A260662 _G. C. Greubel_, Nov 13 2015