login
A266567
Decimal expansion of the generalized Glaisher-Kinkelin constant A(20).
19
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
OFFSET
-58,1
COMMENTS
Also known as the 20th Bendersky constant.
LINKS
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)).
Sequence in context: A055594 A276173 A197631 * A282624 A179858 A141501
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Dec 31 2015
STATUS
approved