A388763 Decimal expansion of (1/32) * exp(3*Pi/4) * sqrt(2) * Gamma(5/8)^3 * (1+sqrt(2)) / Pi^(3/4) / Gamma(7/8)^3.

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

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} A213624(k) / exp(k*Pi).

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

Example

1.0884674689257645171882566709950306570...

Mathematica

First[RealDigits[((2 + Sqrt[2])*Exp[(3*Pi)/4]*Gamma[5/8]^3)/(32*Pi^(3/4)*Gamma[7/8]^3), 10, 100]]
RealDigits[Sqrt[Sqrt[2] - 1] * E^(3*Pi/4) * Gamma[1/4]^3 / (2^(9/2)*Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/32) * exp(3/4 * Pi) * sqrt(2) * gamma(5/8)^3 * (1+2^(1/2)) / Pi^(3/4) / gamma(7/8)^3

Crossrefs

Cf. A213624.

Sequence in context: A126600 A388192 A254615 * A388483 A388884 A388598

Adjacent sequences: A388760 A388761 A388762 * A388764 A388765 A388766

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved