A388450 Decimal expansion of (3/4) * exp(-Pi / 2) * Gamma(2/3)^2 * Gamma(3/4)^2 * (1+3^(1/2))^2 / Gamma(11/12)^2 / Pi.

9, 1, 5, 4, 3, 2, 9, 4, 4, 8, 6, 0, 4, 3, 2, 3, 2, 7, 2, 7, 1, 0, 3, 8, 7, 3, 2, 4, 3, 1, 8, 5, 0, 9, 4, 0, 4, 3, 1, 3, 5, 9, 6, 1, 4, 2, 5, 8, 2, 6, 0, 6, 1, 6, 3, 9, 2, 6, 2, 4, 0, 0, 3, 4, 8, 0, 7, 1, 4, 4, 6, 7, 4, 3, 5, 6, 8, 0, 3, 2, 6, 1, 3, 0, 4, 6, 3

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Formula

Empirical: Equals Sum_{k>=0} A062243(k) / exp(k*Pi).

Equals sqrt(9 + 6*sqrt(3)) / exp(Pi/2). - Vaclav Kotesovec, Jan 08 2026

Example

0.91543294486043232727103873243185094043...

Mathematica

First[RealDigits[(216*(2 + Sqrt[3])*Exp[-1/2*Pi]*Gamma[2/3]^2*Gamma[3/4]^2)/(Pi*Gamma[-1/12]^2), 10, 100]]
RealDigits[Sqrt[9 + 6*Sqrt[3]]/E^(Pi/2), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (3/4) * exp(-Pi / 2) * gamma(2/3)^2 * gamma(3/4)^2 * (1+3^(1/2))^2 / gamma(11/12)^2 / Pi

Crossrefs

Cf. A062243.

Sequence in context: A388901 A388466 A388888 * A143296 A198355 A205326

Adjacent sequences: A388447 A388448 A388449 * A388451 A388452 A388453

Keyword

nonn,cons

Author

Simon Plouffe, Sep 17 2025

Status

approved