A307106 - OEIS

%I #8 Mar 26 2019 03:11:07

%S 1,8,3,6,9,2,1,9,0,8,5,9,5,6,6,3,7,8,3,2,6,5,6,4,0,8,8,0,1,1,2,1,7,0,

%T 3,4,3,1,6,2,5,6,4,6,6,2,4,5,3,5,4,4,9,0,4,4,5,7,0,4,1,7,2,7,5,9,7,0,

%U 7,9,3,4,8,9,6,5,5,1,3,5,1,8,7,5,3,0,9,6,3,6,4,4,4,7,3,6,8,0,4,2,4,7,8,5,4

%N Decimal expansion of Sum_{k>=2} (-1)^k * Zeta(k)^3 / k.

%C Sum_{k>=2} (-1)^k*Zeta(k)/k = A001620 (see MathWorld, formula 122).

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>

%e 1.8369219085956637832656408801121703431625646624535449044570417275970793489...

%p evalf(Sum((-1)^j*Zeta(j)^3/j, j=2..infinity), 120);

%t NSum[(-1)^k*Zeta[k]^3/k, {k, 2, Infinity}, WorkingPrecision -> 200, NSumTerms -> 100000]

%o (PARI) sumalt(k=2, (-1)^k*zeta(k)^3/k)

%Y Cf. A306769, A306774, A306778, A306907.

%K nonn,cons

%O 1,2

%A _Vaclav Kotesovec_, Mar 25 2019