A388571 Decimal expansion of -(1/12) * exp(Pi) * Pi^2 * Gamma(11/12)^2 * (-2+3^(1/2)) / Gamma(2/3)^2 / Gamma(3/4)^6.

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

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} A121456(k) / exp(k*Pi).

Equals sqrt(2*sqrt(3) - 3) * exp(Pi) * Gamma(1/4)^4 / (96*Pi^3). - Vaclav Kotesovec, Jan 08 2026

Example

0.91513748063857091523877677007849521039...

Mathematica

First[RealDigits[-1/12*((-2 + Sqrt[3])*Pi^2*Exp[Pi]*Gamma[11/12]^2)/(Gamma[2/3]^2*Gamma[3/4]^6), 10, 100]]
RealDigits[Sqrt[2*Sqrt[3] - 3]*E^Pi*Gamma[1/4]^4 / (96*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) -(1/12) * exp(Pi) * Pi^2 * gamma(11/12)^2 * (-2+3^(1/2)) / gamma(2/3)^2 / gamma(3/4)^6

Crossrefs

Cf. A121456.

Sequence in context: A298512 A192930 A010168 * A388939 A393233 A340004

Adjacent sequences: A388568 A388569 A388570 * A388572 A388573 A388574

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved