A388574 Decimal expansion of -(1/3) * exp(2*Pi/3) * Pi^(3/2) * Gamma(11/12)^2 * (-2+3^(1/2)) / Gamma(2/3)^2 / Gamma(3/4)^4.

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

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} A122856(k) / exp(k*Pi).

Equals sqrt(2*sqrt(3) - 3) * exp(2*Pi/3) * Gamma(1/4)^2 / (12*Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.0882955937129287636666841455654075959...

Mathematica

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

Prog

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

Crossrefs

Cf. A122856.

Sequence in context: A377589 A011464 A019871 * A174235 A372776 A185266

Adjacent sequences: A388571 A388572 A388573 * A388575 A388576 A388577

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved