A266557 Decimal expansion of the generalized Glaisher-Kinkelin constant A(10).

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

Offset

1,4

Comments

Also known as the 10th Bendersky constant.

Links

G. C. Greubel, Table of n, a(n) for n = 1..2002

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(10) = exp(-zeta'(-10)) = exp((B(10)/4)*(zeta(11)/zeta(10))).

A(10) = exp(10! * Zeta(11) / (2^11 * Pi^10)). - Vaclav Kotesovec, Jan 01 2016

Example

1.01911023332938385372216470498629751351348137284099604...

Mathematica

Exp[N[(BernoulliB[10]/4)*(Zeta[11]/Zeta[10]), 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)), A266558 (A(11)), A266559 (A(12)), A260662 (A(13)), A266560 (A(14)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).

Cf. A013668, A013669, A266261, A027641, A027642.

Sequence in context: A176522 A219732 A259314 * A010534 A078297 A189788

Adjacent sequences: A266554 A266555 A266556 * A266558 A266559 A266560

Keyword

nonn,cons

Author

G. C. Greubel, Dec 31 2015

Status

approved