OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.19 Vallée's Constant, p. 161.
LINKS
Wikipedia, Continuant polynomial.
FORMULA
p_2 = Sum_{i >= 1}(sum_{j >= 1} 1/((i*j + 1)^2*(i*j + i + 1)^2)).
p_2 = Sum_{n >= 0} (-1)^n*(n + 1)*zeta(n + 4)*(zeta(n + 2) - 1).
EXAMPLE
0.04848080144946363270572493388247655633305600669523713977...
MATHEMATICA
digits = 101; s = NSum[(-1)^n*(n + 1)*Zeta[n + 4]*(Zeta[n + 2] - 1), {n, 0, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits + 10]; p2 = -5 + 2*Pi^2/3 - 2*Zeta[3] + 2*s; Join[{0}, RealDigits[p2, 10, digits] // First]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 12 2014
STATUS
approved