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

Author

Jean-François Alcover, Sep 12 2014

Keywords

• nonn
• cons

Examples

			0.04848080144946363270572493388247655633305600669523713977...
		

References

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

Links

• Wikipedia, Continuant polynomial.

Crossrefs

Cf. A074903, A145426.

Programs

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]

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).