A388575 Decimal expansion of (1/4) * exp(Pi / 3) * sqrt(Pi) * Gamma(11/12)^3 * Gamma(7/12)^3 / Gamma(3/4)^8.

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

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

Formula

Empirical: Equals Sum_{k>=0} A122865(k) / exp(k*Pi).

Equals exp(Pi/3) * Gamma(1/4)^2 / (2^(3/2) * 3^(3/4) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.0433824427218395374508069872683740398...

Mathematica

First[RealDigits[(Sqrt[Pi]*Exp[Pi/3]*Gamma[7/12]^3*Gamma[11/12]^3)/(4*Gamma[3/4]^8), 10, 100]]
RealDigits[E^(Pi/3)*Gamma[1/4]^2 / (2^(3/2)*3^(3/4)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/4) * exp(Pi / 3) * sqrt(Pi) * gamma(11/12)^3 * gamma(7/12)^3 / gamma(3/4)^8

Crossrefs

Cf. A122865.

Sequence in context: A038627 A379356 A155835 * A388523 A138187 A105342

Adjacent sequences: A388572 A388573 A388574 * A388576 A388577 A388578

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved