A345384 Decimal expansion of Sum_{k>=2} (-1)^k * zeta''(k).

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

Offset: 1

Author

Vaclav Kotesovec, Jun 17 2021

Keywords

• nonn
• cons

Examples

			1.797744327618368050843854084033051615798915710844403144091653059609067...
		

Links

• Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 528.

Crossrefs

Cf. A085361, A345385.

Programs

Maple

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

Mathematica

RealDigits[Sum[(-1)^k*Zeta''[k], {k, 2, 1000}], 10, 110][[1]]

PARI

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

Formula

Equals Sum_{k>=1} log(k)^2 / (k*(k+1)).