A266567 - OEIS

A266567

Decimal expansion of the generalized Glaisher-Kinkelin constant A(20).

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

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OFFSET

-58,1

COMMENTS

Also known as the 20th Bendersky constant.

LINKS

G. C. Greubel, Table of n, a(n) for n = -58..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(20) = exp((B(20)/4)*(zeta(21)/zeta(20))) = exp(-zeta'(-20)).

A(20) = exp(-20! * Zeta(21) / (2^21 * Pi^20)). - Vaclav Kotesovec, Jan 01 2016

EXAMPLE

3.55707255100437095401897714717491103463878008580889....*10^(-58)

MATHEMATICA

Exp[N[(BernoulliB[20]/4)*(Zeta[21]/Zeta[20]), 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)), A266565 (A(18)), A266566 (A(19)).

Cf. A013678, A266275, A027641, A027642.

Sequence in context: A055594 A276173 A197631 * A282624 A179858 A141501

Adjacent sequences: A266564 A266565 A266566 * A266568 A266569 A266570

KEYWORD

nonn,cons

AUTHOR

G. C. Greubel, Dec 31 2015

STATUS

approved