A388084 - OEIS

%I #8 Sep 25 2025 18:28:28

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

%T 9,0,4,7,9,3,1,3,0,0,7,2,1,0,6,8,2,7,1,8,4,4,6,3,0,4,8,8,8,7,3,6,2,4,

%U 8,5,3,0,3,0,7,3,5,4,1,9,3,9,1,2,7,1,5

%N Decimal expansion of (1/512) * exp(Pi) * Pi^6 / Gamma(3/4)^24.

%H Simon Plouffe, <a href="https://plouffe.fr/articles/numbers%20in%20the%20base_exp_english%202025.pdf">Numbers in the base e^Pi</a>, 2025.

%F Empirical: Equals Sum_{k>=0} A000594(k) / exp(k*Pi).

%e 0.33051755959632854743859758293255229047...

%t First[RealDigits[(Pi^6*Exp[Pi])/(512*Gamma[3/4]^24), 10, 100]]

%o (PARI) 1/512 * exp(Pi) * Pi^6 / gamma(3/4)^24

%Y Cf. A000594.

%K nonn,cons

%O 0,1

%A _Simon Plouffe_, Sep 14 2025