A238166 Decimal expansion of sum_(n>=1) H(n,2)/n^4 where H(n,2) = A007406(n)/A007407(n) is the n-th harmonic number of order 2.

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

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 16.

Formula

Equals zeta(3)^2 - zeta(6)/3.

Example

1.1058264444388178540088457688766809845497962424196...

Mathematica

RealDigits[Zeta[3]^2 - 1/3*Zeta[6], 10, 100][[1]]

Prog

(PARI) zeta(3)^2-Pi^6/2835 /* Michel Marcus, Jul 04 2014 */

Crossrefs

Cf. A007406, A007407, A152648, A152649, A152651, A238167, A238168, A238169.

Sequence in context: A276627 A119420 A134469 * A227417 A260061 A199379

Adjacent sequences: A238163 A238164 A238165 * A238167 A238168 A238169

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Feb 19 2014

Status

approved