A388738 Decimal expansion of (Pi^(5/2) * exp(Pi / 2)) / (3^(1/4) * Gamma(7/12)^5 * Gamma(11/12)^5).

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

Offset

1,1

Links

Table of n, a(n) for n=1..87.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A204342(k) / exp(k*Pi).

Equals 3 * exp(Pi/2) * Gamma(1/4)^10 / (2^(15/2) * Pi^(15/2)). - Vaclav Kotesovec, Jan 08 2026

Example

5.8448203826931346236164576679822537206...

Mathematica

First[RealDigits[(Pi^(5/2)*Exp[Pi/2])/(3^(1/4)*Gamma[7/12]^5*Gamma[11/12]^5), 10, 100]]
RealDigits[3*E^(Pi/2)*Gamma[1/4]^10 / (2^(15/2)*Pi^(15/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/3) * exp(Pi / 2) * Pi^(5/2) * 3^(3/4) / gamma(11/12)^5 / gamma(7/12)^5
(PARI) 3*exp(Pi/2)*gamma(1/4)^10/(2^(15/2)*Pi^(15/2)) \\ Charles R Greathouse IV, Jul 14 2026

Crossrefs

Cf. A204342.

Sequence in context: A366072 A394008 A019649 * A224833 A246926 A199288

Adjacent sequences: A388735 A388736 A388737 * A388739 A388740 A388741

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved