A388397 Decimal expansion of (24 * (3+2 * sqrt(3)) * Gamma(2/3)^2) / (Gamma(-1/12)^2 * Gamma(3/4)^2).

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

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} A034896(k) / exp(k*Pi).

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

Example

1.1807216414311911665305728766138124055...

Mathematica

First[RealDigits[(24*(3 + 2*Sqrt[3])*Gamma[2/3]^2)/(Gamma[-1/12]^2*Gamma[3/4]^2), 10, 100]]
RealDigits[Sqrt[3 + 2*Sqrt[3]]*Gamma[1/4]^4 / (12*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A034896.

Sequence in context: A292887 A154461 A261613 * A165268 A306071 A389655

Adjacent sequences: A388394 A388395 A388396 * A388398 A388399 A388400

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved