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A240264 Decimal expansion of sum_(n=1..infinity) (-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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Eric Weisstein's MathWorld, Harmonic Number

FORMULA

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

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

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-Fran├žois Alcover, Apr 03 2014

STATUS

approved

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Last modified January 22 16:27 EST 2020. Contains 331152 sequences. (Running on oeis4.)