A307106 Decimal expansion of Sum_{k>=2} (-1)^k * Zeta(k)^3 / k.

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, 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, 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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's MathWorld, Riemann Zeta Function

Wikipedia, Riemann Zeta Function

Example

1.8369219085956637832656408801121703431625646624535449044570417275970793489...

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A306769, A306774, A306778, A306907.

Sequence in context: A132035 A153813 A316166 * A372857 A277775 A199719

Adjacent sequences: A307103 A307104 A307105 * A307107 A307108 A307109

Keyword

nonn,cons

Author

Vaclav Kotesovec, Mar 25 2019

Status

approved