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A243265 Decimal expansion of the generalized Glaisher-Kinkelin constant A(5). 27
1, 0, 0, 9, 6, 8, 0, 3, 8, 7, 2, 8, 5, 8, 6, 6, 1, 6, 1, 1, 2, 0, 0, 8, 9, 1, 9, 0, 4, 6, 2, 6, 3, 0, 6, 9, 2, 6, 0, 3, 2, 7, 6, 3, 4, 7, 2, 1, 1, 5, 2, 4, 9, 1, 8, 4, 6, 0, 9, 2, 4, 7, 2, 1, 5, 6, 2, 3, 0, 1, 4, 2, 5, 0, 0, 3, 4, 1, 0, 0, 3, 2, 7, 7, 0, 1, 5, 0, 5, 6, 5, 9, 6, 5, 2, 7, 6, 4, 5, 5, 5, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Also known as the 5th Bendersky constant.

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..2004

Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant

FORMULA

A(k) = exp(B(k+1)/(k+1)*H(k)-zeta'(-k)), where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number.

A(5) = exp(137/15120-zeta'(-5)).

Equals exp(gamma/252 - 15*Zeta'(6)/(4*Pi^6)) * (2*Pi)^(1/252), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 25 2015

EXAMPLE

1.00968038728586616112008919046263...

MATHEMATICA

RealDigits[Exp[137/15120-Zeta'[-5]], 10, 103] // First

RealDigits[Exp[N[(BernoulliB[6]/6)*(EulerGamma + Log[2*Pi] - Zeta'[6]/Zeta[6]), 200]]]//First (* G. C. Greubel, Dec 31 2015 *)

CROSSREFS

Cf. A255344, A259070.

Cf. A019727, A074962, A243262, A243263, A243264, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.

Sequence in context: A019643 A011012 A157989 * A248472 A306553 A011194

Adjacent sequences:  A243262 A243263 A243264 * A243266 A243267 A243268

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 02 2014

STATUS

approved

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Last modified March 29 21:29 EDT 2020. Contains 333117 sequences. (Running on oeis4.)