A256988 Decimal expansion of Sum_{k>=1} H(k)^3/k^2 where H(k) is the k-th harmonic number.
1, 2, 3, 4, 6, 5, 8, 1, 9, 0, 1, 7, 3, 0, 9, 9, 5, 3, 8, 1, 5, 1, 0, 7, 4, 0, 3, 0, 6, 0, 5, 5, 4, 6, 7, 2, 5, 2, 6, 5, 2, 9, 6, 0, 6, 6, 1, 6, 7, 9, 2, 6, 2, 3, 2, 8, 4, 3, 7, 7, 4, 9, 0, 5, 6, 0, 9, 2, 7, 5, 0, 9, 3, 2, 0, 0, 9, 4, 1, 9, 0, 5, 3, 3, 0, 2, 8, 1, 5, 4, 3, 8, 0, 9, 3, 0, 8, 2, 9, 7, 1, 1, 6, 8
Offset: 2
Examples
12.346581901730995381510740306055467252652960661679262328437749...
Links
- Alois Panholzer and Helmut Prodinger, Computer-free evaluation of an infinite double sum via Euler sums Séminaire Lotharingien de Combinatoire 55 (2005), Article B55a
- Eric Weisstein's MathWorld, Harmonic Number.
Programs
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Mathematica
RealDigits[10*Zeta[5] + (Pi^2/6)*Zeta[3], 10, 104] // First
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PARI
10*zeta(5) + zeta(2)*zeta(3) \\ Michel Marcus, Apr 14 2015
Formula
Equals 10*zeta(5) + zeta(2)*zeta(3) or, 10*zeta(5) + (Pi^2/6)*zeta(3).