A266560 Decimal expansion of the generalized Glaisher-Kinkelin constant A(14).

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

Offset

1,2

Comments

Also known as the 14th 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(14) = exp(-zeta'(-14)) = exp((B(14)/4)*(zeta(15)/zeta(14))).

A(14) = exp(14! * Zeta(15) / (2^15 * Pi^14)). - Vaclav Kotesovec, Jan 01 2016

Example

1.338644754241536299558046958873255142542092537062742480234...

Mathematica

Exp[N[(BernoulliB[14]/4)*(Zeta[15]/Zeta[14]), 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)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).

Cf. A013672, A013673, A266264, A027641, A027642.

Sequence in context: A267092 A272212 A319133 * A021751 A302675 A305841

Adjacent sequences: A266557 A266558 A266559 * A266561 A266562 A266563

Keyword

nonn,cons

Author

G. C. Greubel, Dec 31 2015

Status

approved