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%I A266567 #19 Mar 27 2024 20:11:37
%S A266567 3,5,5,7,0,7,2,5,5,1,0,0,4,3,7,0,9,5,4,0,1,8,9,7,7,1,4,7,1,7,4,9,1,1,
%T A266567 0,3,4,6,3,8,7,8,0,0,8,5,8,0,8,8,9,1,7,9,5,7,5,7,9,6,4,4,0,0,7,3,2,1,
%U A266567 1,4,2,0,2,4,2,9,5,7,0,1,2,0,7,4,8,9,1,3,0,1,5,7,8
%N A266567 Decimal expansion of the generalized Glaisher-Kinkelin constant A(20).
%C A266567 Also known as the 20th Bendersky constant.
%H A266567 G. C. Greubel, <a href="/A266567/b266567.txt">Table of n, a(n) for n = -58..2000</a>
%F A266567 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 A266567 A(20) = exp((B(20)/4)*(zeta(21)/zeta(20))) = exp(-zeta'(-20)).
%F A266567 A(20) = exp(-20! * Zeta(21) / (2^21 * Pi^20)). - _Vaclav Kotesovec_, Jan 01 2016
%e A266567 3.55707255100437095401897714717491103463878008580889....*10^(-58)
%t A266567 Exp[N[(BernoulliB[20]/4)*(Zeta[21]/Zeta[20]), 200]]
%Y A266567 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)).
%Y A266567 Cf. A013678, A266275, A027641, A027642.
%K A266567 nonn,cons
%O A266567 -58,1
%A A266567 _G. C. Greubel_, Dec 31 2015

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