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

Author

G. C. Greubel, Dec 31 2015

Keywords

• nonn
• cons

Comments

Also known as the 6th Bendersky constant.

Examples

			1.00591719699867346844401398355425565639061565500693211400980...
		

Links

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

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

Programs

Mathematica

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

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