%I #23 Apr 17 2026 02:39:30

%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]]

%o (PARI) exp(bernfrac(6) * zeta(7) / (4 * zeta(6))) \\ _Amiram Eldar_, Apr 17 2026

%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