A266553 - OEIS

%I #20 Mar 27 2024 20:11:49

%S 1,0,0,5,9,1,7,1,9,6,9,9,8,6,7,3,4,6,8,4,4,4,0,1,3,9,8,3,5,5,4,2,5,5,

%T 6,5,6,3,9,0,6,1,5,6,5,5,0,0,6,9,3,2,1,1,4,0,0,9,8,0,5,1,5,7,4,0,8,1,

%U 4,6,8,7,0,3,4,2,9,9,4,6,3,2,7,7,1,9,6,7,0,8,1,7,0,8,8,4,1,4,6,8,7,3,5,4,1,1,1,0,0,2,2,4,0,3

%N Decimal expansion of the generalized Glaisher-Kinkelin constant A(6).

%C Also known as the 6th Bendersky constant.

%H G. C. Greubel, <a href="/A266553/b266553.txt">Table of n, a(n) for n = 1..2003</a>

%F 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 A(6) = exp(- zeta'(-6)) = exp((B(6)/4)*(zeta(7)/zeta(6))).

%F A(6) = exp(6! * Zeta(7) / (2^7 * Pi^6)). - _Vaclav Kotesovec_, Jan 01 2016

%e 1.00591719699867346844401398355425565639061565500693211400980...

%t Exp[N[(BernoulliB[6]/4)*(Zeta[7]/Zeta[6]), 200]]

%Y Cf. A019727 (A(0)), A074962 (A(1)), A243262 (A(2)), A243263 (A(3)), A243264 (A(4)), A243265 (A(5)), 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 Cf. A013664, A013665, A259071, A027641, A027642

%K nonn,cons

%O 1,4

%A _G. C. Greubel_, Dec 31 2015