A233090 Decimal expansion of Sum_{n>=1} (-1)^(n-1)*H(n)/n^2, where H(n) is the n-th harmonic number.

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

Offset

0,1

Links

Table of n, a(n) for n=0..99.

Philippe Flajolet and Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998), page 32.

Formula

Equals 5*zeta(3)/8.

Equals -Integral_{x=0..1} (log(1+x)*log(1-x)/x)*dx. - Amiram Eldar, May 06 2023

Example

0.7512855644747464283748363509446562442281164327128118011201697220886...

Mathematica

RealDigits[ 5*Zeta[3]/8, 10, 100] // First

Crossrefs

Cf. A002117 (zeta(3)), A197070 (3*zeta(3)/4), A233091 (7*zeta(3)/8), A076788 (alternating sum with denominator n), A152648 (non-alternating sum with denominator n^2), A152649 (non-alternating sum with denominator n^3), A233033 (alternating sum with denominator n^3).

Sequence in context: A093205 A156536 A110191 * A254177 A021575 A334632

Adjacent sequences: A233087 A233088 A233089 * A233091 A233092 A233093

Keyword

nonn,cons

Author

Jean-François Alcover, Dec 04 2013, after the comment by Peter Bala about A233033.

Status

approved