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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.
1
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
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
Sequence in context: A195494 A154969 A192741 * A119743 A272643 A243424
KEYWORD
nonn,cons
AUTHOR
STATUS
approved