cp's OEIS Frontend

A383851 Decimal expansion of exp(8*G/Pi)*((1 - exp(-Pi/2))/(1 + exp(-Pi/2)))^2, where G is Catalan's constant (A006752).

%I A383851 #11 May 14 2025 14:09:34
%S A383851 4,4,3,1,2,0,1,3,0,7,1,9,4,1,9,9,1,9,7,0,8,2,3,6,7,7,2,8,3,5,5,2,8,7,
%T A383851 2,9,3,2,8,3,8,0,1,5,2,8,1,0,1,2,2,7,4,7,3,5,6,3,2,0,9,2,1,4,3,8,9,6,
%U A383851 8,0,7,5,8,5,8,7,0,0,3,6,5,3,8,3,2,5,6,4,2,0
%N A383851 Decimal expansion of exp(8*G/Pi)*((1 - exp(-Pi/2))/(1 + exp(-Pi/2)))^2, where G is Catalan's constant (A006752).
%H A383851 Paolo Xausa, <a href="/A383851/b383851.txt">Table of n, a(n) for n = 1..10000</a>
%H A383851 Michael Penn, <a href="https://www.youtube.com/watch?v=Dg0LhegZtBY">A beautiful Ramanujan product</a>, YouTube video, 2025.
%F A383851 Equals Product_{i=0..oo} (1 + 4/(2*i+1)^4)^((-1)^i*(2*i+1)) (from Ramanujan).
%e A383851 4.4312013071941991970823677283552872932838015281012...
%t A383851 First[RealDigits[Exp[8*Catalan/Pi]*((1 - #)/(1 + #))^2 & [Exp[-Pi/2]], 10, 100]]
%Y A383851 Cf. A006752, A049006, A377753.
%K A383851 nonn,cons,easy
%O A383851 1,1
%A A383851 _Paolo Xausa_, May 13 2025