A244667 Decimal expansion of sum_(n>=1) (H(n)^3/(n+1)^2) where H(n) is the n-th harmonic number.
9, 7, 5, 4, 2, 6, 2, 5, 1, 3, 8, 7, 2, 5, 7, 0, 5, 6, 5, 6, 8, 2, 3, 2, 6, 5, 8, 9, 9, 1, 2, 8, 8, 1, 8, 3, 2, 5, 1, 0, 2, 5, 8, 3, 6, 2, 9, 2, 4, 4, 8, 0, 2, 9, 8, 5, 0, 2, 2, 6, 7, 3, 6, 1, 3, 3, 3, 2, 4, 1, 9, 5, 7, 5, 4, 3, 7, 1, 5, 3, 4, 1, 9, 0, 2, 7, 0, 7, 6, 7, 1, 7, 0, 0, 2, 4, 9, 6, 3, 0, 2
Offset: 1
Examples
9.75426251387257056568232658991288183251025836292448029850226736133324...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 27.
Programs
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Magma
SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); Pi(R)^2/6*Evaluate(L,3) + 15/2*Evaluate(L,5); // G. C. Greubel, Aug 31 2018
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Mathematica
RealDigits[15/2*Zeta[5] + Zeta[2]*Zeta[3], 10, 101] // First
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PARI
default(realprecision, 100); Pi^2/6*zeta(3) + 15/2*zeta(5) \\ G. C. Greubel, Aug 31 2018
Formula
Equals Pi^2/6*zeta(3) + 15/2*zeta(5).