A388494 Decimal expansion of (2^(7/8) * sqrt((2-sqrt(2)) * Pi) * exp(-Pi/24) * Gamma(7/8)^2) / Gamma(5/8)^2.

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

Offset

1,2

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} A100534(k) / exp(k*Pi).

Equals 2^(9/8) * sqrt(1 + sqrt(2)) * Pi^(3/2) / (exp(Pi/24) * Gamma[1/4]^2). - Vaclav Kotesovec, Jan 08 2026

Example

1.2593899752732958463945950915505202759...

Mathematica

First[RealDigits[(2^(7/8)*Sqrt[(2 - Sqrt[2])*Pi]*Exp[-1/24*Pi]*Gamma[7/8]^2)/Gamma[5/8]^2, 10, 100]]
RealDigits[2^(9/8)*Sqrt[1 + Sqrt[2]]*Pi^(3/2)/(E^(Pi/24)*Gamma[1/4]^2), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) 2 * exp(-1/24 * Pi) * sqrt(Pi) * 2^(3/8) * gamma(7/8)^2 / gamma(5/8)^2 / (2+2^(1/2))^(1/2)

Crossrefs

Cf. A100534.

Sequence in context: A333530 A111474 A388098 * A111761 A388352 A021798

Adjacent sequences: A388491 A388492 A388493 * A388495 A388496 A388497

Keyword

nonn,cons

Author

Simon Plouffe, Sep 17 2025

Status

approved