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A266560
Decimal expansion of the generalized Glaisher-Kinkelin constant A(14).
19
1, 3, 3, 8, 6, 4, 4, 7, 5, 4, 2, 4, 1, 5, 3, 6, 2, 9, 9, 5, 5, 8, 0, 4, 6, 9, 5, 8, 8, 7, 3, 2, 5, 5, 1, 4, 2, 5, 4, 2, 0, 9, 2, 5, 3, 7, 0, 6, 2, 7, 4, 2, 4, 8, 0, 2, 3, 4, 0, 6, 2, 0, 9, 4, 5, 8, 9, 7, 9, 5, 3, 1, 5, 2, 8, 5, 1, 9, 6, 4, 8, 4, 5, 5, 2, 4, 5, 2, 9, 3, 1, 3, 9, 8, 7
OFFSET
1,2
COMMENTS
Also known as the 14th Bendersky constant.
LINKS
FORMULA
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.
A(14) = exp(-zeta'(-14)) = exp((B(14)/4)*(zeta(15)/zeta(14))).
A(14) = exp(14! * Zeta(15) / (2^15 * Pi^14)). - Vaclav Kotesovec, Jan 01 2016
EXAMPLE
1.338644754241536299558046958873255142542092537062742480234...
MATHEMATICA
Exp[N[(BernoulliB[14]/4)*(Zeta[15]/Zeta[14]), 200]]
CROSSREFS
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)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).
Sequence in context: A267092 A272212 A319133 * A021751 A302675 A305841
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Dec 31 2015
STATUS
approved