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A233033 Decimal expansion of sum_(n=1..infinity) (-1)^(n-1)*H(n)/n^3 where H(n) is the n-th harmonic number. 2
8, 5, 9, 2, 4, 7, 1, 5, 7, 9, 2, 8, 5, 9, 0, 6, 1, 5, 5, 3, 9, 9, 0, 9, 9, 3, 9, 4, 7, 5, 7, 5, 9, 9, 8, 0, 7, 1, 2, 8, 8, 4, 3, 5, 0, 8, 6, 0, 4, 1, 4, 9, 2, 6, 7, 6, 0, 5, 2, 0, 6, 8, 9, 7, 6, 6, 3, 8, 3, 4, 8, 1, 5, 3, 3, 4, 8, 9, 2, 3, 3, 0, 7, 1, 1, 3, 8, 8, 3, 8, 1, 5, 1, 8, 8, 4, 3, 0, 6, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 32.

FORMULA

Equals 11*Pi^4/360 +1/12*Pi^2*log(2)^2 -log(2)^4/12 -2*Li4(1/2) -7/4*log(2)*zeta(3).

Also, equals 1/2*integral_{z=0..1} (log(z)^2*log(1+z)) / (z*(1+z)) dz.

EXAMPLE

0.859247157928590615539909939475759980712884350860414926760520689766...

MATHEMATICA

RealDigits[ 11*Pi^4/360 + 1/12*Pi^2*Log[2]^2 - Log[2]^4/12 - 2*PolyLog[4, 1/2] - 7/4*Log[2]*Zeta[3], 10, 100] // First

PROG

(PARI) 11*Pi^4/360 + Pi^2*log(2)^2/12 - log(2)^4/12 - 2*polylog(4, 1/2) - 7*log(2)*zeta(3)/4 \\ Charles R Greathouse IV, Aug 27 2014

CROSSREFS

Cf. A076788 (same alternating sum with denominator n), A152648 (non-alternating sum with denominator n^2), A152649 (non-alternating sum with denominator n^3).

Sequence in context: A074071 A100126 A330111 * A244810 A273985 A132036

Adjacent sequences:  A233030 A233031 A233032 * A233034 A233035 A233036

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Dec 03 2013

STATUS

approved

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Last modified March 28 12:31 EDT 2020. Contains 333085 sequences. (Running on oeis4.)