%I #19 Nov 21 2020 16:59:06

%S 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,

%T 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,

%U 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

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

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

%H Simon Plouffe, <a href="http://www.plouffe.fr">Simon Plouffe Home Page</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/AlmostInteger.html">Almost Integer</a>

%e 10.00000000000000019016176788866267558435930585544533348025489784340610994387...

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

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

%K nonn,cons

%O 2,19

%A _Jean-François Alcover_, May 27 2013

%E Offset corrected by _Rick L. Shepherd_, Jan 01 2014