A240264 - OEIS

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

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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