A388443 Decimal expansion of (1/32) * exp(5*Pi/8) * 2^(7/8) * Gamma(5/8)^2 * (2+sqrt(2)) * (2-sqrt(2))^(1/2) / sqrt(Pi) / Gamma(7/8)^2.

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

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} A053692(k) / exp(k*Pi).

Equals exp(5*Pi/8) * Gamma(1/4)^2 / (2^(27/8) * sqrt(1 + sqrt(2)) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.0432982626193107505557582450704474899...

Mathematica

First[RealDigits[(Exp[(5*Pi)/8]*Gamma[5/4]^2*Root[-32 + 32*#1^4 + #1^8 & , 2, 0])/Pi^(3/2), 10, 100]]
RealDigits[E^(5*Pi/8) * Gamma[1/4]^2 / (2^(27/8) * Sqrt[1 + Sqrt[2]] * Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A053692.

Sequence in context: A388820 A273991 A388444 * A292828 A388524 A020703

Adjacent sequences: A388440 A388441 A388442 * A388444 A388445 A388446

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved