A241753 Decimal expansion of Sum_{n>=1} (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

Offset: 1

Author

Jean-François Alcover, Apr 28 2014

Keywords

• nonn
• cons

Examples

			2.97638889270563002666901016548821173263...
		

Links

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

Crossrefs

Cf. A218505.

Programs

Mathematica

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

PARI

11*Pi^4/360 \\ Stefano Spezia, May 26 2025

Formula

Equals 1/(2*Pi)*Integral_{x=0..Pi} (Pi-t)^2*log(2*sin(t/2))^2 dt.

Equals 11/17*A218505.

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