A241753 - OEIS

A241753

Decimal expansion of sum_(n=1..infinity) (H(n)/(n+1))^2, where H(n) is the n-th harmonic number.

2, 9, 7, 6, 3, 8, 8, 8, 9, 2, 7, 0, 5, 6, 3, 0, 0, 2, 6, 6, 6, 9, 0, 1, 0, 1, 6, 5, 4, 8, 8, 2, 1, 1, 7, 3, 2, 6, 3, 0, 5, 6, 5, 1, 1, 7, 7, 7, 6, 4, 9, 8, 9, 9, 6, 1, 2, 8, 1, 8, 4, 5, 9, 2, 4, 7, 1, 3, 3, 1, 6, 9, 4, 5, 1, 4, 1, 6, 4, 3, 2, 8, 0, 3, 1, 5, 0, 1, 4, 9, 8, 8, 3, 9, 6, 7, 4, 7, 7, 2

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OFFSET

1,1

LINKS

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

David H. Bailey and Jonathan M. Borwein, Experimental Mathematics: Examples, Methods and Implications, Notices of the AMS Volume 52, Number 5, page 506.

FORMULA

1/(2*Pi)*integral_(0..Pi) (Pi-t)^2*log(2*sin(t/2))^2 dt.

11/17*A218505.

11*Pi^4/360. - Vaclav Kotesovec, Apr 28 2014

EXAMPLE

2.97638889270563002666901016548821173263...

MATHEMATICA

RealDigits[11*Pi^4/360, 10, 100] // First

CROSSREFS

Cf. A218505.

Sequence in context: A180310 A268086 A021340 * A157350 A121837 A160439

Adjacent sequences: A241750 A241751 A241752 * A241754 A241755 A241756

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Apr 28 2014

STATUS

approved