A240264 Decimal expansion of Sum_{n >= 1} (-1)^(n+1)*H(n,2)/n^2, where H(n,2) is the n-th harmonic number of order 2.

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

Offset

0,1

References

B. C. Berndt, Ramanujan's Notebooks Part I, Springer-Verlag,

Links

Table of n, a(n) for n=0..99.

Eric Weisstein's World of Mathematics, Harmonic Number

Formula

Equals zeta(3) - Pi^2/12*log(2).

Let a(p,q) = Sum_{n >= 1} (-1)^(n+1)*H(n,p)/n^q, then A076788 is a(1,1), A233090 is a(1,2) and this sequence is a(2,1).

Equals Sum_{n >= 1} (1/2)^n * H(n,1)/n^2, where H(n,1) = Sum_{k = 1..n} 1/k. See Berndt, p. 258. - Peter Bala, Oct 28 2021

Example

0.631966197838...

Mathematica

Zeta[3] - Pi^2/12*Log[2] // RealDigits[#, 10, 100]& // First

Prog

(PARI) zeta(3)-log(2)*Pi^2/12 \\ Charles R Greathouse IV, Apr 03 2014

Crossrefs

Cf. A076788, A233090.

Sequence in context: A195494 A154969 A192741 * A119743 A272643 A243424

Adjacent sequences: A240261 A240262 A240263 * A240265 A240266 A240267

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 03 2014

Status

approved