A238168 Decimal expansion of sum_(n>=1) H(n)^2/n^5 where H(n) is the n-th harmonic number.

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

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 6*zeta(7) - zeta(2)*zeta(5) - 5/2*zeta(3)*zeta(4).

Example

1.091882588664530085165782130699273873...

Mathematica

RealDigits[6*Zeta[7] -Zeta[2]*Zeta[5] -(5/2)*Zeta[3]*Zeta[4], 10, 100][[1]]

Prog

(PARI) 6*zeta(7) - zeta(2)*zeta(5) - (5/2)*zeta(3)*zeta(4) \\ G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A152648, A152649, A152651, A238166, A238167, A238169.

Sequence in context: A191502 A109871 A087500 * A340551 A299622 A163899

Adjacent sequences: A238165 A238166 A238167 * A238169 A238170 A238171

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 19 2014

Status

approved