A266553 - OEIS

A266553

Decimal expansion of the generalized Glaisher-Kinkelin constant A(6).

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

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OFFSET

1,4

COMMENTS

Also known as the 6th Bendersky constant.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..2003

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(6) = exp(- zeta'(-6)) = exp((B(6)/4)*(zeta(7)/zeta(6))).

A(6) = exp(6! * zeta(7) / (2^7 * Pi^6)). - Vaclav Kotesovec, Jan 01 2016

EXAMPLE

1.00591719699867346844401398355425565639061565500693211400980...

MATHEMATICA

Exp[N[(BernoulliB[6]/4)*(Zeta[7]/Zeta[6]), 200]]

PROG

(PARI) exp(bernfrac(6) * zeta(7) / (4 * zeta(6))) \\ Amiram Eldar, Apr 17 2026

CROSSREFS