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A218505 Decimal expansion of sum_{k=1..infinity} (H(k)/k)^2, where H(k) = sum_{j=1..k} 1/j. 6
4, 5, 9, 9, 8, 7, 3, 7, 4, 3, 2, 7, 2, 3, 3, 7, 3, 1, 3, 9, 4, 3, 0, 1, 5, 7, 1, 0, 2, 9, 9, 9, 6, 3, 5, 8, 6, 7, 9, 2, 6, 9, 1, 5, 4, 5, 6, 5, 4, 5, 8, 9, 3, 5, 7, 6, 5, 2, 6, 4, 8, 9, 1, 5, 6, 3, 7, 5, 1, 2, 6, 1, 8, 7, 9, 4, 6, 1, 7, 5, 9, 7, 8, 6, 6, 8, 6, 5, 9, 5, 2, 7, 5, 2, 2, 2, 4, 6, 4, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, decimal expansion of 17/(22*Pi)*integral_{t=0..Pi} ((Pi-t)^2*log(2*sin(t/2))^2 dt.

LINKS

Table of n, a(n) for n=1..100.

D. H. Bailey and J. M. Borwein, Euler's Multi-Zeta Sums

FORMULA

Equals 17*zeta(4)/4 = 17*Pi^4/360 = (17/4) * sum_{k=1..infinity} 1/k^4.

EXAMPLE

4.5998737432723373139430157102999635867926915456545893...

MATHEMATICA

17*Pi^4/360 // N[#, 100] & // RealDigits // First

CROSSREFS

Sequence in context: A021689 A178610 A197268 * A128891 A172180 A193959

Adjacent sequences:  A218502 A218503 A218504 * A218506 A218507 A218508

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Mar 28 2013

EXTENSIONS

Offset corrected by Rick L. Shepherd, Jan 01 2014

STATUS

approved

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Last modified February 26 10:40 EST 2021. Contains 341631 sequences. (Running on oeis4.)