cp's OEIS Frontend

A373506 Decimal expansion of 4*Pi/3^(3/2) - Pi^2/9.

%I A373506 #19 Jun 10 2024 03:52:06
%S A373506 1,3,2,1,7,7,6,4,4,1,0,8,0,1,3,9,5,0,9,8,1,0,4,9,4,2,3,2,4,2,5,5,2,4,
%T A373506 1,8,3,5,6,6,1,2,1,7,2,9,9,8,5,7,8,8,4,7,5,6,0,2,8,0,7,7,6,0,9,3,7,4,
%U A373506 9,2,5,9,4,5,6,6,3,3,7,9,2,9,0,2,3,0,8
%N A373506 Decimal expansion of 4*Pi/3^(3/2) - Pi^2/9.
%H A373506 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 A373506 Equals Sum_{n>=0} 1/((n+1)*binomial(2n,n)).
%F A373506 The alternating case is Sum_{n>=0} (-1)^n/((n+1)*binomial(2*n,n)) = 8*log(phi)/sqrt(5)-4*log^2(phi) = 0.79537... where phi is the golden ratio.
%F A373506 Equals A275486 - A100044. - _Stefano Spezia_, Jun 07 2024
%e A373506 1.321776441080139509810494232425524183566...
%p A373506 4*Pi/3^(3/2)-Pi^2/9 ; evalf(%) ;
%t A373506 RealDigits[4*Pi/3^(3/2) - Pi^2/9, 10, 120][[1]] (* _Amiram Eldar_, Jun 10 2024 *)
%o A373506 (PARI) 4*Pi/3^(3/2) - Pi^2/9 \\ _Amiram Eldar_, Jun 10 2024
%Y A373506 Cf. A100044, A275486, A073016 (no n+1 denominator), A073010 (denominator n), A373507 (denominator n-1).
%K A373506 cons,nonn
%O A373506 1,2
%A A373506 _R. J. Mathar_, Jun 07 2024