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

1,1

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.

Formula

Equals Pi^2/6*zeta(3) + 15/2*zeta(5).

Example

9.75426251387257056568232658991288183251025836292448029850226736133324...

Mathematica

RealDigits[15/2*Zeta[5] + Zeta[2]*Zeta[3], 10, 101] // First

Prog

(PARI)  default(realprecision, 100); Pi^2/6*zeta(3) + 15/2*zeta(5) \\ G. C. Greubel, Aug 31 2018
(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

Crossrefs

Cf. A001008, A002805, A002117, A013663.

Sequence in context: A114433 A222129 A188141 * A307235 A194554 A065467

Adjacent sequences: A244664 A244665 A244666 * A244668 A244669 A244670

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 04 2014

Status

approved