A306769 Decimal expansion of Sum_{k>=2} (-1)^k * Zeta(k)^2 / k.

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

Offset: 1

Author

Vaclav Kotesovec, Mar 09 2019

Keywords

• nonn
• cons

Comments

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

Examples

			1.043402917574288733255289646671676030548470866046882561044570479769585...
		

Links

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

Crossrefs

Cf. A231132, A306760, A306765, A306774, A306778, A307106.

Programs

Maple

evalf(Sum((-1)^j*Zeta(j)^2/j, j=2..infinity), 100);

Mathematica

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

PARI

sumalt(k=2, (-1)^k*zeta(k)^2/k) \\ Michel Marcus, Mar 09 2019

Formula

Equals log(A306765) + A001620^2.