A247318 Decimal expansion of p_2, a probability associated with continuant polynomials.

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.19 Vallée's Constant, p. 161.

Links

Table of n, a(n) for n=0..101.

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

Cf. A074903, A145426.

Sequence in context: A160204 A200392 A195289 * A019838 A155970 A348573

Adjacent sequences: A247315 A247316 A247317 * A247319 A247320 A247321

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 12 2014

Status

approved