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)).
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Dec 31 2015
STATUS
approved