A256988 Decimal expansion of Sum_{k>=1} H(k)^3/k^2 where H(k) is the k-th harmonic number.

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

References

Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2021, p. 225, eq. (4.113).

Links

Table of n, a(n) for n=2..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.

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.26, p. 294, eq. (4.34), section 5.26, p. 320, section 6.26, pp. 401-406.

Eric Weisstein's MathWorld, Harmonic Number.

Index entries for sequences related to harmonic numbers.

Formula

Equals 10*zeta(5) + zeta(2)*zeta(3) = 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

Crossrefs

Cf. A001008, A002805.

Cf. A002117, A013661, A013663, A152648, A152651, A238181, A244667, A256987.

Sequence in context: A129258 A360633 A395364 * A104650 A083179 A391106

Adjacent sequences: A256985 A256986 A256987 * A256989 A256990 A256991

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 14 2015

Status

approved