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A266566 Decimal expansion of the generalized Glaisher-Kinkelin constant A(19). 20
1, 7, 8, 2, 7, 5, 4, 2, 7, 6, 9, 4, 6, 7, 1, 4, 1, 1, 8, 8, 1, 7, 6, 7, 0, 9, 7, 7, 4, 3, 5, 4, 4, 5, 5, 6, 9, 5, 6, 0, 8, 1, 8, 3, 7, 0, 1, 5, 7, 2, 0, 6, 5, 3, 2, 4, 4, 8, 9, 4, 4, 3, 5, 5, 0, 0, 6, 2, 9, 3, 8, 8, 9, 6, 5, 8, 7, 4, 0, 6, 6, 7, 1, 9, 8, 4, 0, 6, 0, 9, 8, 4, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-28,2

COMMENTS

Also known as the 19th Bendersky constant.

LINKS

G. C. Greubel, Table of n, a(n) for n = -28..2000

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(19) = exp(H(19)*B(20)/20 - zeta'(-19)) = exp((B(20)/20)*(EulerGamma + log(2*Pi) - (zeta'(20)/zeta(20))).

EXAMPLE

1.78275427694671411881767097743544556956081837015720653244894...*10^(-28)

MATHEMATICA

Exp[N[(BernoulliB[20]/20)*(EulerGamma + Log[2*Pi] - Zeta'[20]/Zeta[20]), 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)), A266565 (A(18)), A266567 (A(20)).

Sequence in context: A021565 A011103 A245758 * A309523 A153622 A257576

Adjacent sequences:  A266563 A266564 A266565 * A266567 A266568 A266569

KEYWORD

nonn,cons

AUTHOR

G. C. Greubel, Dec 31 2015

STATUS

approved

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Last modified September 20 22:20 EDT 2019. Contains 327252 sequences. (Running on oeis4.)