cp's OEIS Frontend

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

%I A145436 #13 Jul 01 2024 13:17:24
%S A145436 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,
%T A145436 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,
%U A145436 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
%N A145436 Decimal expansion of Sum_{n>=0} (-1)^n/((2n+1)^2*binomial(2n,n)).
%D A145436 Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.45.
%D A145436 Bruce C. Berndt, Ramanujan's Notebooks, Part 1, Springer-Verlag, 1985, Chapter 9, p. 289, eq. (vii).
%D A145436 Calvin C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers, Springer, 2013. See p. 222.
%F A145436 Equals A013661 - 3*A002390^2.
%e A145436 0.95023960511664325898162795295142690916973085105890...
%p A145436 1/6*Pi^2-3*ln(1/2+1/2*5^(1/2))^2 ;
%t A145436 RealDigits[Zeta[2] - 3 * Log[GoldenRatio]^2, 10, 120][[1]] (* _Amiram Eldar_, May 06 2023 *)
%o A145436 (PARI) Pi^2/6-3*log(1/2+sqrt(5)/2)^2 \\ _Charles R Greathouse IV_, Sep 13 2013
%Y A145436 Cf. A000984, A002390, A013661, A294486.
%K A145436 cons,easy,nonn
%O A145436 0,1
%A A145436 _R. J. Mathar_, Feb 08 2009