A388917 Decimal expansion of (1/48) * exp(11*Pi/12) * Pi^(3/2) * 2^(1/4) * 3^(1/2) * Gamma(11/12)^4 * Gamma(7/12)^3 * (3^(1/2)-1) / Gamma(2/3) / Gamma(3/4)^11.

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

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} A260295(k) / exp(k*Pi).

Equals exp(11*Pi/12) * Gamma(1/4)^4 / (16 * 3^(9/8) * sqrt(1 + sqrt(3)) * Pi^3). - Vaclav Kotesovec, Jan 09 2026

Example

1.0905039083727564123479581731975108481...

Mathematica

First[RealDigits[-1/24*((-3 + Sqrt[3])*Pi^(3/2)*Exp[(11*Pi)/12]*Gamma[7/12]^3*Gamma[11/12]^4)/(2^(3/4)*Gamma[2/3]*Gamma[3/4]^11), 10, 100]]
RealDigits[E^(11*Pi/12)*Gamma[1/4]^4 / (16*3^(9/8)*Sqrt[1 + Sqrt[3]]*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (1/48) * exp(11/12 * Pi) * Pi^(3/2) * 2^(1/4) * 3^(1/2) * gamma(11/12)^4 * gamma(7/12)^3 * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)^11

Crossrefs

Cf. A260295.

Sequence in context: A301865 A388577 A370705 * A388471 A309605 A010770

Adjacent sequences: A388914 A388915 A388916 * A388918 A388919 A388920

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved