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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. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Adjacent sequences:  A256984 A256985 A256986 * A256988 A256989 A256990

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Apr 14 2015

STATUS

approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)