A388557 Decimal expansion of ((-1+sqrt(3))^3 * Pi^2 * exp(Pi) * Gamma(11/12)^3) / (6 * sqrt(6) * Gamma(2/3)^3 * Gamma(3/4)^5).

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

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} A113447(k) / exp(k*Pi).

Equals exp(Pi) * Gamma(1/4)^2 / (2^(7/4) * 3^(9/8) * (1 + sqrt(3))^(3/2) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.0450008254980492546672197316256716293...

Mathematica

First[RealDigits[((-1 + Sqrt[3])^3*Pi^2*Exp[Pi]*Gamma[11/12]^3)/(6*Sqrt[6]*Gamma[2/3]^3*Gamma[3/4]^5), 10, 100]]
RealDigits[E^Pi*Gamma[1/4]^2 / (2^(7/4)*3^(9/8)*(1 + Sqrt[3])^(3/2)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/36) * exp(Pi) * Pi^2*3^(1/2) * gamma(11/12)^3 * sqrt(2) * (3^(1/2)-1)^3 / gamma(2/3)^3 / gamma(3/4)^5

Crossrefs

Cf. A113447.

Sequence in context: A024247 A067445 A167003 * A335762 A254294 A143574

Adjacent sequences: A388554 A388555 A388556 * A388558 A388559 A388560

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved