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%I #17 Jul 16 2021 11:29:17
%S 2,9,9,6,5,5,2,9,8,3,1,3,9,2,3,5,1,9,3,9,4,3,1,8,6,5,2,9,7,2,7,4,2,0,
%T 1,7,9,1,9,0,8,2,2,6,1,0,9,1,1,5,5,6,5,9,1,5,8,8,1,8,7,1,6,6,8,2,0,5,
%U 7,6,1,6,0,2,8,6,7,6,7,7,6,1,1,7,2,6,8,7,3,6,3,0,3,4
%N Decimal expansion of zeta'(-19) (the derivative of Riemann's zeta function at -19) (negated).
%H G. C. Greubel, <a href="/A266274/b266274.txt">Table of n, a(n) for n = 2..1500</a>
%F zeta'(-n) = (BernoulliB(n+1)*HarmonicNumber(n))/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant.
%F zeta'(-19) = -48069674759189/512143632000 - log(A(19)).
%e -29.965529831392351939431865297274201791908226109115565915881....
%t RealDigits[N[Zeta'[-19], 100]]
%Y 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)), A266270 (zeta'(-15)), A266271 (zeta'(-16)), A266272 (zeta'(-17)), A266273 (zeta'(-18)), A266275 (zeta'(-20)).
%K nonn,cons
%O 2,1
%A _G. C. Greubel_, Dec 26 2015
%E Offset corrected by _Rick L. Shepherd_, May 30 2016
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