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

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]]

Crossrefs

Cf. A019727 (A(0)), A074962 (A(1)), A243262 (A(2)), A243263 (A(3)), A243264 (A(4)), A243265 (A(5)), 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)), A266567 (A(20)).

Cf. A013664, A013665, A259071, A027641, A027642

Sequence in context: A362742 A010490 A021173 * A306980 A063921 A346044

Adjacent sequences: A266550 A266551 A266552 * A266554 A266555 A266556

Keyword

nonn,cons

Author

G. C. Greubel, Dec 31 2015

Status

approved