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URL: https://oeis.org/A266559

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A266559
Decimal expansion of the generalized Glaisher-Kinkelin constant A(12).
19
9, 3, 8, 6, 8, 9, 4, 4, 5, 5, 9, 6, 0, 1, 2, 5, 8, 5, 1, 5, 2, 9, 6, 5, 7, 8, 1, 3, 2, 0, 6, 7, 6, 7, 1, 8, 3, 3, 3, 2, 5, 8, 7, 6, 8, 5, 2, 1, 8, 3, 5, 0, 0, 9, 8, 6, 6, 3, 9, 0, 7, 1, 6, 3, 4, 2, 4, 0, 5, 8, 8, 3, 7, 3, 8, 0, 1, 5, 1, 1, 7, 0, 8, 6, 7, 6, 4, 0, 2, 1
OFFSET
0,1
COMMENTS
Also known as the 12th 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(12) = exp(-zeta'(-12)) = exp((B(12)/4)*(zeta(13)/zeta(12))).
A(12) = exp(-12! * Zeta(13) / (2^13 * Pi^12)). - Vaclav Kotesovec, Jan 01 2016
EXAMPLE
0.9386894455960125851529657813206767183332587685218350098663907...
MATHEMATICA
RealDigits[Exp[N[(BernoulliB[12]/4)*(Zeta[13]/Zeta[12]), 200]]][[1]] (* Program amended by Harvey P. Dale, Aug 16 2021 *)
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)), A260662 (A(13)), A266560 (A(14)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).
Sequence in context: A394059 A387979 A358942 * A381694 A372837 A111971
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Dec 31 2015
STATUS
approved