A218505 Decimal expansion of Sum_{k>=1} (H(k)/k)^2, where H(k) = Sum_{j=1..k} 1/j.

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

Offset

1,1

Links

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

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

Index entries for transcendental numbers

Formula

Equals 17*zeta(4)/4.

Equals 17*Pi^4/360.

Equals (17/4) * Sum_{k>=1} 1/k^4.

Equals (17/(22*Pi)) * Integral_{t=0..Pi} (Pi-t)^2*log(2*sin(t/2))^2 dt.

Example

4.5998737432723373139430157102999635867926915456545893...

Mathematica

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

Prog

(PARI) 17*Pi^4/360 \\ Charles R Greathouse IV, Sep 02 2024

Crossrefs

Sequence in context: A021689 A178610 A197268 * A128891 A172180 A193959

Adjacent sequences: A218502 A218503 A218504 * A218506 A218507 A218508

Keyword

nonn,cons

Author

Jean-François Alcover, Mar 28 2013

Extensions

Offset corrected by Rick L. Shepherd, Jan 01 2014

Status

approved