A388616 Decimal expansion of (1/72) * exp(2*Pi/3) * Gamma(2/3)^2 * (1+3^(1/2))^2 / Gamma(11/12)^2 / Gamma(3/4)^2.

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

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} A134079(k) / exp(k*Pi).

Equals (1 + sqrt(3)) * exp(2*Pi/3) * Gamma(1/4)^4 / (2^(7/2) * 3^(9/4) * Pi^3). - Vaclav Kotesovec, Jan 08 2026

Example

0.92261366267702216499245625766110800932...

Mathematica

First[RealDigits[(4*(2 + Sqrt[3])*Exp[(2*Pi)/3]*Gamma[2/3]^2)/(Gamma[-1/12]^2*Gamma[3/4]^2), 10, 100]]
RealDigits[(1 + Sqrt[3])*E^(2*Pi/3)*Gamma[1/4]^4 / (2^(7/2)*3^(9/4)*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/72) * exp(2/3 * Pi) * gamma(2/3)^2 * (1+3^(1/2))^2 / gamma(11/12)^2 / gamma(3/4)^2

Crossrefs

Cf. A134079.

Sequence in context: A379385 A080994 A392290 * A340809 A200298 A110543

Adjacent sequences: A388613 A388614 A388615 * A388617 A388618 A388619

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved