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A256988
Decimal expansion of Sum_{k>=1} H(k)^3/k^2 where H(k) is the k-th harmonic number.
1
1, 2, 3, 4, 6, 5, 8, 1, 9, 0, 1, 7, 3, 0, 9, 9, 5, 3, 8, 1, 5, 1, 0, 7, 4, 0, 3, 0, 6, 0, 5, 5, 4, 6, 7, 2, 5, 2, 6, 5, 2, 9, 6, 0, 6, 6, 1, 6, 7, 9, 2, 6, 2, 3, 2, 8, 4, 3, 7, 7, 4, 9, 0, 5, 6, 0, 9, 2, 7, 5, 0, 9, 3, 2, 0, 0, 9, 4, 1, 9, 0, 5, 3, 3, 0, 2, 8, 1, 5, 4, 3, 8, 0, 9, 3, 0, 8, 2, 9, 7, 1, 1, 6, 8
OFFSET
2,2
LINKS
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
Equals 10*zeta(5) + zeta(2)*zeta(3) or, 10*zeta(5) + (Pi^2/6)*zeta(3).
EXAMPLE
12.346581901730995381510740306055467252652960661679262328437749...
MATHEMATICA
RealDigits[10*Zeta[5] + (Pi^2/6)*Zeta[3], 10, 104] // First
PROG
(PARI) 10*zeta(5) + zeta(2)*zeta(3) \\ Michel Marcus, Apr 14 2015
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved