A238167 - OEIS

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

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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]]