OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1500
FORMULA
zeta'(-n) = (BernoulliB(n+1)*HarmonicNumber(n))/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant.
zeta'(-15) = -4325053069/2940537600 - log(A(15)).
EXAMPLE
-0.400319302807725593843580317520320367201261286266232944284106942....
MATHEMATICA
RealDigits[N[Zeta'[-15], 100]]
CROSSREFS
Cf. A075700 (zeta'(0)), A084448 (zeta'(-1)), A240966 (zeta'(-2)), A259068 (zeta'(-3)), A259069 (zeta'(-4)), A259070 (zeta'(-5)), A259071 (zeta'(-6)), A259072 (zeta'(-7)), A259073 (zeta'(-8)), A266260 (zeta'(-9)), A266261 (zeta'(-10)), A266262 (zeta'(-11)), A266263 (zeta'(-12)), A260660 (zeta'(-13)), A266264 (zeta'(-14)), A266271 (zeta'(-16)), A266272 (zeta'(-17)), A266273 (zeta'(-18)), A266274 (zeta'(-19)), A266275 (zeta'(-20)).
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Dec 25 2015
STATUS
approved