A145436 Decimal expansion of Sum_{n>=0} (-1)^n/((2n+1)^2*binomial(2n,n)).

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

Offset: 0

Author

R. J. Mathar, Feb 08 2009

Keywords

• cons
• easy
• nonn

Examples

			0.95023960511664325898162795295142690916973085105890...
		

References

• Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.45.
• Bruce C. Berndt, Ramanujan's Notebooks, Part 1, Springer-Verlag, 1985, Chapter 9, p. 289, eq. (vii).
• Calvin C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers, Springer, 2013. See p. 222.

Crossrefs

Cf. A000984, A002390, A013661, A294486.

Programs

Maple

1/6*Pi^2-3*ln(1/2+1/2*5^(1/2))^2 ;

Mathematica

RealDigits[Zeta[2] - 3 * Log[GoldenRatio]^2, 10, 120][[1]] (* Amiram Eldar, May 06 2023 *)

PARI

Pi^2/6-3*log(1/2+sqrt(5)/2)^2 \\ Charles R Greathouse IV, Sep 13 2013

Formula

Equals A013661 - 3*A002390^2.