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

Author

Vaclav Kotesovec, Mar 25 2019

Keywords

• nonn
• cons

Comments

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

Examples

			1.8369219085956637832656408801121703431625646624535449044570417275970793489...
		

Links

• Eric Weisstein's MathWorld, Riemann Zeta Function
• Wikipedia, Riemann Zeta Function

Crossrefs

Cf. A306769, A306774, A306778, A306907.

Programs

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]

PARI

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