A388918 Decimal expansion of (1/32) * exp(Pi / 8) * 2^(5/8) * Gamma(2/3)^5 * Gamma(7/12)^(3/2) * 3^(1/8) * (5*3^(1/2)+9) / Pi^2 / Gamma(11/12)^(7/2).

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

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} A260308(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(3)) * exp(Pi/8) * Gamma(1/4)^2 / (2^(15/8) * 3^(3/8) * Pi^(3/2)). - Vaclav Kotesovec, Jan 09 2026

Example

1.0434630110395058900130685715613743235...

Mathematica

First[RealDigits[(3^(1/8)*(9 + 5*Sqrt[3])*Exp[Pi/8]*Gamma[7/12]^(3/2)*Gamma[2/3]^5)/(16*2^(3/8)*Pi^2*Gamma[11/12]^(7/2)), 10, 100]]
RealDigits[Sqrt[1 + Sqrt[3]]*E^(Pi/8)*Gamma[1/4]^2 / (2^(15/8)*3^(3/8)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (1/32) * exp(Pi / 8) * 2^(5/8) * gamma(2/3)^5 * gamma(7/12)^(3/2) * 3^(1/8) * (5*3^(1/2)+9) / Pi^2 / gamma(11/12)^(7/2)

Crossrefs

Cf. A260308.

Sequence in context: A135103 A369052 A282822 * A193694 A354471 A117893

Adjacent sequences: A388915 A388916 A388917 * A388919 A388920 A388921

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved