A244665 Decimal expansion of sum_(n>=1) (H(n,3)/n^3) where H(n,3) = A007408(n)/A007409(n) is the n-th harmonic number of order 3.

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

Offset

1,2

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 23.

Formula

zeta(3)^2/2 + Pi^6/1890.

Example

1.2311419302090416868141015042989541775427764478983711179869214129514580195...

Mathematica

RealDigits[1/2*Zeta[3]^2 + 1/2*Zeta[6], 10, 103] // First

Prog

(PARI) zeta(3)^2/2 + Pi^6/1890 \\ Michel Marcus, Jul 04 2014

Crossrefs

Cf. A002117, A007408, A007409, A244664.

Sequence in context: A059247 A340940 A362464 * A194518 A023572 A023570

Adjacent sequences: A244662 A244663 A244664 * A244666 A244667 A244668

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 04 2014

Status

approved