A388388 Decimal expansion of (sqrt(58+41 * sqrt(2)) * exp(Pi) * Gamma(5/8)^6) / (256 * Pi^(3/2) * Gamma(7/8)^6).

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

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} A030207(k) / exp(k*Pi).

Equals sqrt(2 - sqrt(2)) * exp(Pi) * Gamma(1/4)^6 / (256 * Pi^(9/2)). - Vaclav Kotesovec, Jan 08 2026

Example

0.91016067657431845046021879463297338267...

Mathematica

First[RealDigits[(Sqrt[58 + 41*Sqrt[2]]*Exp[Pi]*Gamma[5/8]^6)/(256*Pi^(3/2)*Gamma[7/8]^6), 10, 100]]
RealDigits[Sqrt[2 - Sqrt[2]]*E^Pi*Gamma[1/4]^6 / (256*Pi^(9/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/512) * exp(Pi) * sqrt(2) * gamma(5/8)^6 * (7 * sqrt(2)+10) * (2-2^(1/2))^(1/2) / Pi^(3/2) / gamma(7/8)^6

Crossrefs

Cf. A030207.

Sequence in context: A256667 A175764 A388595 * A388816 A388468 A388863

Adjacent sequences: A388385 A388386 A388387 * A388389 A388390 A388391

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved