A091349 Decimal expansion of Sum_{m>=1, n>=1} 1/(m^2*(m^2 + m*n + n^2)).

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

Offset

1,4

Links

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

Eric Weisstein's World of Mathematics, Double Series

Example

1.0044...

Mathematica

digits = 100; Pi^4/36 - EulerGamma*Zeta[3] + NSum[ (-3 - I*Sqrt[3])/6*PolyGamma[(2 + n - I*Sqrt[3]*n)/2]/n^3 + (-3 + I*Sqrt[3])/6*PolyGamma[(2 + n + I*Sqrt[3]*n)/2]/n^3, {n, 1, Infinity}, NSumTerms -> digits + 20, WorkingPrecision -> digits + 20, AccuracyGoal -> digits + 20, PrecisionGoal -> digits + 20, Method -> {"EulerMaclaurin", Method ->{"NIntegrate", "MaxRecursion" -> 20}}] // Re // RealDigits[#, 10, digits] & // First (* Jean-François Alcover, Feb 11 2013 *)

Crossrefs

Sequence in context: A019527 A062836 A137903 * A103483 A170934 A079999

Adjacent sequences: A091346 A091347 A091348 * A091350 A091351 A091352

Keyword

nonn,cons

Author

Eric W. Weisstein, Feb 03 2004

Extensions

More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008

More terms from Jean-François Alcover, Feb 11 2013

Status

approved