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

Author

G. C. Greubel, Dec 31 2015

Keywords

• nonn
• cons

Comments

Also known as the 18th Bendersky constant.

Examples

			929840.411822940088043113785037604334445353815966558489979361...
		

Links

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

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.

Programs

Mathematica

Exp[N[(BernoulliB[18]/4)*(Zeta[19]/Zeta[18]), 200]]

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