A266565 Decimal expansion of the generalized Glaisher-Kinkelin constant A(18).

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

G. C. Greubel, Table of n, a(n) for n = 6..2007

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)).

Cf. A013676, A013677, A266273, A027641, A027642.

Sequence in context: A242743 A197812 A146492 * A090298 A248315 A256658

Adjacent sequences: A266562 A266563 A266564 * A266566 A266567 A266568

Keyword

nonn,cons

Author

G. C. Greubel, Dec 31 2015

Status

approved