A238167 Decimal expansion of sum_(n>=1) H(n,3)/n^5 where H(n,3) = A007408(n)/A007409(n) is the n-th harmonic number of order 3.

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

Offset

1,3

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 5*zeta(2)*zeta(5) + 2*zeta(3)*zeta(4) - 10*zeta(7).

Example

1.046924401724676082345723014222792329619598402264...

Mathematica

RealDigits[5*Zeta[2]*Zeta[5] +2*Zeta[3]*Zeta[4] -10*Zeta[7], 10, 100][[1]]

Prog

(PARI) 5*zeta(2)*zeta(5) + 2*zeta(3)*zeta(4) - 10*zeta(7) \\ G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A007408, A007409, A152648, A152649, A152651, A238166, A238168, A238169.

Sequence in context: A239634 A175013 A210616 * A307036 A076418 A059910

Adjacent sequences: A238164 A238165 A238166 * A238168 A238169 A238170

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 19 2014

Status

approved