A388787 Decimal expansion of (1/64) * exp(Pi) * Pi * Gamma(11/12)^9 * Gamma(7/12)^9 / Gamma(3/4)^22.

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

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

Formula

Empirical: Equals Sum_{k>=0} A226132(k) / exp(k*Pi).

Equals exp(Pi) * Gamma(1/4)^4 / (72*sqrt(2)*3^(1/4)*Pi^3). - Vaclav Kotesovec, Jan 08 2026

Example

0.96232823428717717954968405829557329496...

Mathematica

First[RealDigits[(Pi*Exp[Pi]*Gamma[7/12]^9*Gamma[11/12]^9)/(64*Gamma[3/4]^22), 10, 100]]
RealDigits[E^Pi * Gamma[1/4]^4 / (72*Sqrt[2]*3^(1/4)*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/64) * exp(Pi) * Pi * gamma(11/12)^9 * gamma(7/12)^9 / gamma(3/4)^22

Crossrefs

Cf. A226132.

Sequence in context: A154899 A335563 A011219 * A202543 A188528 A243257

Adjacent sequences: A388784 A388785 A388786 * A388788 A388789 A388790

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved