A389015 Decimal expansion of (3/16) * Gamma(2/3)^2 * Gamma(11/12)^3 * Gamma(7/12)^5 * (2+3^(1/2)) / Gamma(3/4)^12.

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

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} A282544(k) / exp(k*Pi).

Equals (1 + sqrt(3)) * Gamma(1/4)^4 / (8*sqrt(3)*Pi^3). - Vaclav Kotesovec, Jan 09 2026

Example

1.0987852967628734197825713976781969975...

Mathematica

First[RealDigits[(3*(2 + Sqrt[3])*Gamma[7/12]^5*Gamma[2/3]^2*Gamma[11/12]^3)/(16*Gamma[3/4]^12), 10, 100]]
RealDigits[(1 + Sqrt[3])*Gamma[1/4]^4 / (8*Sqrt[3]*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (3/16) * gamma(2/3)^2 * gamma(11/12)^3 * gamma(7/12)^5 * (2+3^(1/2)) / gamma(3/4)^12

Crossrefs

Cf. A282544.

Sequence in context: A200688 A288239 A163243 * A060799 A094146 A021507

Adjacent sequences: A389012 A389013 A389014 * A389016 A389017 A389018

Keyword

nonn,cons

Author

Simon Plouffe, Sep 22 2025

Status

approved