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

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

Offset: 1

Author

Paolo Xausa, May 13 2025

Keywords

• nonn
• cons
• easy

Examples

			4.4312013071941991970823677283552872932838015281012...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Michael Penn, A beautiful Ramanujan product, YouTube video, 2025.

Crossrefs

Cf. A006752, A049006, A377753.

Programs

Mathematica

First[RealDigits[Exp[8*Catalan/Pi]*((1 - #)/(1 + #))^2 & [Exp[-Pi/2]], 10, 100]]

Formula

Equals Product_{i=0..oo} (1 + 4/(2*i+1)^4)^((-1)^i*(2*i+1)) (from Ramanujan).