A266563 Decimal expansion of the generalized Glaisher-Kinkelin constant A(16).

1, 6, 9, 8, 1, 8, 3, 9, 7, 8, 4, 2, 7, 7, 5, 6, 0, 7, 7, 4, 7, 3, 0, 9, 5, 5, 1, 6, 8, 3, 1, 2, 7, 1, 1, 8, 7, 9, 5, 1, 5, 2, 9, 1, 4, 2, 8, 6, 3, 7, 7, 3, 5, 8, 6, 0, 2, 7, 1, 7, 5, 9, 5, 5, 0, 0, 0, 7, 5, 4, 2, 1, 7, 6, 0, 8, 8, 8, 8, 0, 1, 4, 7, 1, 9, 3, 5, 6, 7, 0, 8, 2

Offset

0,2

Comments

Also known as the 16th Bendersky constant.

Links

G. C. Greubel, Table of n, a(n) for n = 0..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(16) = exp((B(16)/4)*(zeta(17)/zeta(16))) = exp(-zeta'(-16)).

A(16) = exp(-16! * zeta(17) / (2^17 * Pi^16)). - Vaclav Kotesovec, Jan 01 2016

Example

0.16981839784277560774730955168312711879515291428637735860...

Mathematica

Exp[N[(BernoulliB[16]/4)*(Zeta[17]/Zeta[16]), 200]]

Prog

(PARI) exp(bernfrac(16) * zeta(17) / (4 * zeta(16))) \\ Amiram Eldar, Apr 17 2026

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)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).

Cf. A013674, A013675, A266271, A027641, A027642.

Sequence in context: A019696 A119801 A191608 * A382197 A383955 A335028

Adjacent sequences: A266560 A266561 A266562 * A266564 A266565 A266566

Keyword

nonn,cons

Author

G. C. Greubel, Dec 31 2015

Status

approved