A388677 Decimal expansion of (3/32) * exp(Pi / 2) * Pi * Gamma(11/12)^7 * Gamma(7/12)^7 / Gamma(3/4)^18.

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

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A159819(k) / exp(k*Pi).

Equals exp(Pi/2) * Gamma(1/4)^4 / (2^(7/2) * 3^(3/4) * Pi^3). - Vaclav Kotesovec, Jan 07 2026

Example

1.0394819037745574802700803092636638549...

Mathematica

First[RealDigits[3*Exp[Pi/2]*Pi*Gamma[11/12]^7*Gamma[7/12]^7/(32*Gamma[3/4]^18), 10, 100]] (* Paolo Xausa, Sep 19 2025 *)
RealDigits[E^(Pi/2)*Gamma[1/4]^4 / (2^(7/2)*3^(3/4)*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 07 2026 *)

Prog

(PARI) (3/32) * exp(Pi / 2) * Pi * gamma(11/12)^7 * gamma(7/12)^7 / gamma(3/4)^18
(PARI) sqrt(2) / (16 * 3^(3/4)) * exp(Pi/2) * gamma(1/4)^4 / Pi^3 \\ Charles R Greathouse IV, Jul 10 2026

Crossrefs

Cf. A159819.

Sequence in context: A212002 A199452 A388340 * A388887 A249414 A011428

Adjacent sequences: A388674 A388675 A388676 * A388678 A388679 A388680

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved