A256987 - OEIS

A256987

Decimal expansion of Sum_{k>=1} H(k)*H(k,2)/k^2 where H(k) is the k-th harmonic number and H(k,2) the k-th harmonic number of order 2.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

Alois Panholzer and Helmut Prodinger, Computer-free evaluation of an infinite double sum via Euler sums, Séminaire Lotharingien de Combinatoire 55 (2005), Article B55a

Eric Weisstein's MathWorld, Harmonic Number.

FORMULA

zeta(5) + zeta(2)*zeta(3) = zeta(5) + (Pi^2/6)*zeta(3).

EXAMPLE

3.01423210544066604452845092794215974013923238616204702067...

MATHEMATICA

RealDigits[Zeta[5] + (Pi^2/6)*Zeta[3], 10, 105] // First

PROG

(PARI) zeta(5) + zeta(2)*zeta(3) \\ Michel Marcus, Apr 14 2015

CROSSREFS

Cf. A002117, A013661, A013663, A152648, A152651, A238181, A244667, A256988.

Sequence in context: A226912 A177330 A197126 * A048963 A119458 A106356