A226120 Decimal expansion of Sum_{n>=1} n^3/(exp(2*Pi*n/7)-1).

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

Offset: 2

Author

Jean-François Alcover, May 27 2013

Keywords

• nonn
• cons

Comments

An almost-integer discovered by Simon Plouffe. The computed sum equals 10 within 15 digits.

Examples

			10.00000000000000019016176788866267558435930585544533348025489784340610994387...
		

Links

• Simon Plouffe, Simon Plouffe Home Page
• Eric Weisstein's MathWorld, Almost Integer

Crossrefs

Cf. A060295 (famous almost-integer: Ramanujan's constant), A226121 (another surprising almost-integer by Simon Plouffe), A007775, A089034.

Programs

Mathematica

NSum[n^3/(Exp[2*Pi*n/7] - 1), {n, 1, Infinity}, NSumTerms -> 220,    WorkingPrecision -> 100] // RealDigits[#, 10, 100] & // First

Extensions

Offset corrected by Rick L. Shepherd, Jan 01 2014