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A266565
Decimal expansion of the generalized Glaisher-Kinkelin constant A(18).
19
9, 2, 9, 8, 4, 0, 4, 1, 1, 8, 2, 2, 9, 4, 0, 0, 8, 8, 0, 4, 3, 1, 1, 3, 7, 8, 5, 0, 3, 7, 6, 0, 4, 3, 3, 4, 4, 4, 5, 3, 5, 3, 8, 1, 5, 9, 6, 6, 5, 5, 8, 4, 8, 9, 9, 7, 9, 3, 6, 1, 1, 4, 8, 0, 2, 9, 7, 2, 4, 8, 3, 6, 0, 3, 6, 8, 0, 0, 5, 9, 0, 5, 2, 0, 6, 1, 7, 1, 9, 7, 2, 1, 4
OFFSET
6,1
COMMENTS
Also known as the 18th 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(18) = exp((B(18)/4)*(zeta(19)/zeta(18))) = exp(-zeta'(-18)).
A(18) = exp(18! * Zeta(19) / (2^19 * Pi^18)). - Vaclav Kotesovec, Jan 01 2016
EXAMPLE
929840.411822940088043113785037604334445353815966558489979361...
MATHEMATICA
Exp[N[(BernoulliB[18]/4)*(Zeta[19]/Zeta[18]), 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)), A266560 (A(14)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266566 (A(19)), A266567 (A(20)).
Sequence in context: A242743 A197812 A146492 * A090298 A248315 A256658
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Dec 31 2015
STATUS
approved