A241215 Decimal expansion of Sum_{n>=1} H(n)^4/(n+1)^3 where H(n) is the n-th harmonic number.
1, 8, 0, 1, 6, 1, 3, 2, 6, 8, 0, 4, 3, 4, 1, 2, 9, 0, 3, 7, 2, 9, 4, 8, 8, 9, 4, 2, 0, 2, 0, 8, 8, 8, 4, 3, 0, 3, 1, 3, 7, 7, 5, 8, 2, 7, 7, 8, 7, 8, 9, 3, 3, 0, 0, 8, 7, 3, 3, 9, 4, 9, 2, 5, 4, 8, 0, 4, 4, 4, 8, 1, 8, 8, 4, 0, 8, 9, 3, 3, 3, 7, 5, 3, 0, 9, 4, 5, 7, 4, 3, 3, 0, 4, 2, 7, 1, 9, 3, 1
Offset: 1
Examples
1.80161326804341290372948894202088843...
Links
- Philippe Flajolet and Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998), page 16.
Crossrefs
Programs
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Mathematica
37/180*Pi^4*Zeta[3] - 5/6*Pi^2*Zeta[5] - 109/8*Zeta[7] // RealDigits[#, 10, 100]& // First
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PARI
37/2*zeta(3)*zeta(4) - 5*zeta(2)*zeta(5) - 109/8*zeta(7) \\ Stefano Spezia, Jan 19 2025
Formula
Equals (37/2)*zeta(3)*zeta(4) - 5*zeta(2)*zeta(5) - (109/8)*zeta(7).
Equals (37/180)*Pi^4*zeta(3) - (5/6)*Pi^2*zeta(5) - (109/8)*zeta(7).