A244674 Decimal expansion of sum_(n>=1) (H(n)^3/(n+1)^3) where H(n) is the n-th harmonic number.

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

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 27.

Formula

Equals 2*zeta(3)^2 - 11/5040*Pi^6.

Example

0.79161153152434211716617692742020206556997223833501687696290045428823...

Mathematica

RealDigits[2*Zeta[3]^2 - 33/16*Zeta[6], 10, 102] // First

Prog

(PARI)  default(realprecision, 100);  2*zeta(3)^2 - 11/5040*Pi^6 \\ G. C. Greubel, Aug 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); 2*Evaluate(L, 3)^2 - 11/5040*Pi(R)^6; // G. C. Greubel, Aug 31 2018

Crossrefs

Cf. A001008, A002805, A002117.

Sequence in context: A091900 A222135 A086318 * A130834 A132806 A016629

Adjacent sequences: A244671 A244672 A244673 * A244675 A244676 A244677

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 04 2014

Status

approved