A256987 Decimal expansion of Sum_{k>=1} H(k)*H(k,2)/k^2 where H(k) is the k-th harmonic number and H(k,2) the k-th harmonic number of order 2.
3, 0, 1, 4, 2, 3, 2, 1, 0, 5, 4, 4, 0, 6, 6, 6, 0, 4, 4, 5, 2, 8, 4, 5, 0, 9, 2, 7, 9, 4, 2, 1, 5, 9, 7, 4, 0, 1, 3, 9, 2, 3, 2, 3, 8, 6, 1, 6, 2, 0, 4, 7, 0, 2, 0, 6, 7, 0, 0, 1, 4, 9, 5, 4, 9, 5, 8, 5, 1, 8, 6, 2, 3, 9, 3, 2, 8, 8, 5, 6, 9, 2, 2, 6, 2, 4, 2, 7, 4, 7, 9, 0, 7, 8, 8, 8, 2, 9, 4, 3, 7, 5, 1, 7, 1
Offset: 1
Examples
3.01423210544066604452845092794215974013923238616204702067...
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[Zeta[5] + (Pi^2/6)*Zeta[3], 10, 105] // First
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PARI
zeta(5) + zeta(2)*zeta(3) \\ Michel Marcus, Apr 14 2015
Formula
zeta(5) + zeta(2)*zeta(3) = zeta(5) + (Pi^2/6)*zeta(3).