A238181 Decimal expansion of sum_(n>=1) H(n)^2/n^3 where H(n) is the n-th harmonic number (Quadratic Euler Sum S(2,3)).

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

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 24.

Formula

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

Example

1.6519427927044986239626937611144940161...

Mathematica

7/2*Zeta[5] - Zeta[2]*Zeta[3] // RealDigits[#, 10, 100]& // First

Crossrefs

Cf. A152648, A152649, A152651, A218505, A238168, A238182, A238183.

Sequence in context: A340543 A177824 A242000 * A197517 A102079 A177938

Adjacent sequences: A238178 A238179 A238180 * A238182 A238183 A238184

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 19 2014

Status

approved