cp's OEIS Frontend

A373508 Decimal expansion of sqrt(3)*Pi/6 + Pi^2/36 - 1.

%I A373508 #20 Jun 10 2024 03:46:14
%S A373508 1,8,1,0,5,5,3,5,9,9,2,5,1,4,6,6,6,4,7,0,9,1,0,8,3,2,3,2,6,2,0,8,2,0,
%T A373508 6,4,3,4,5,1,9,1,4,4,0,9,1,4,1,7,0,0,2,7,4,0,7,5,3,5,5,0,5,9,2,2,3,9,
%U A373508 6,1,6,8,9,6,3,7,1,0,4,2,0,8,1,4
%N A373508 Decimal expansion of sqrt(3)*Pi/6 + Pi^2/36 - 1.
%H A373508 Renzo Sprugnoli, <a href="https://www.emis.de/journals/INTEGERS/papers/g27/g27.Abstract.html">Sums of reciprocals of the central binomial coefficients</a>, INTEGERS 6 (2006) #A27.
%F A373508 Equals Sum_{n>=2} 1/((n-1)^2*binomial(2n,n)).
%F A373508 Sum_{n>=2} (-1)^n/((n-1)^2*binomial(2n,n)) = 1 - sqrt(5)*log(phi) + log(phi)^2 = 0.1555... where phi is the golden ratio.
%F A373508 Equals A093766 + A100044/4 - 1. - _Stefano Spezia_, Jun 07 2024
%e A373508 0.181055359925146664709108323262082...
%p A373508 (sqrt(3)+Pi/6)*Pi/6-1; evalf(%) ;
%t A373508 RealDigits[Sqrt[3]*Pi/6 + Pi^2/36 - 1, 10, 120][[1]] (* _Amiram Eldar_, Jun 10 2024 *)
%o A373508 (PARI) sqrt(3)*Pi/6 + Pi^2/36 - 1 \\ _Amiram Eldar_, Jun 10 2024
%Y A373508 Cf. A093766, A100044, A373507 (denominator n-1), A073010 (denominator n).
%K A373508 nonn,cons
%O A373508 0,2
%A A373508 _R. J. Mathar_, Jun 07 2024