A238182 Decimal expansion of sum_(n>=1) H(n)^2/n^4 where H(n) is the n-th harmonic number (Quadratic Euler Sum S(2,4)).

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

Offset

1,2

Comments

No closed form of S(2,2q) is known to date, except for S(2,2) (A218505) and S(2,4) (this sequence).

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

97/24*zeta(6) - 2*zeta(3)^2.

Example

1.221879945319880138518806475290994812569...

Mathematica

97/24*Zeta[6] - 2*Zeta[3]^2 // RealDigits[#, 10, 100]& // First

Crossrefs

Cf. A152648, A152649, A152651, A218505, A238168, A238181, A238183.

Sequence in context: A198569 A135080 A348724 * A117260 A077944 A077992

Adjacent sequences: A238179 A238180 A238181 * A238183 A238184 A238185

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 19 2014

Status

approved