A388900 Decimal expansion of -(1/3) * exp(5*Pi/8) * Pi^(5/4) * 2^(1/4) * Gamma(11/12)^2 * (-2+3^(1/2)) / Gamma(2/3)^2 / Gamma(3/4)^3.

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

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} A259529(k) / exp(k*Pi).

Equals (sqrt(3) - 1) * exp(5*Pi/8) * Gamma(1/4) / (2^(7/4) * (3*Pi)^(3/4)). - Vaclav Kotesovec, Jan 08 2026

Example

1.0450851633671021057344808210577296098...

Mathematica

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

Prog

(PARI) -(1/3) * exp(5/8 * Pi) * Pi^(5/4) * 2^(1/4) * gamma(11/12)^2 * (-2+3^(1/2)) / gamma(2/3)^2 / gamma(3/4)^3

Crossrefs

Cf. A259529.

Sequence in context: A360962 A320162 A388881 * A388337 A354068 A387236

Adjacent sequences: A388897 A388898 A388899 * A388901 A388902 A388903

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved