A388628 - OEIS

%I #10 Jul 10 2026 15:21:22

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

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

%U 6,8,0,6,5,8,0,0,9,9,8,0,0,5,7,8,1,6,0

%N Decimal expansion of (64 * sqrt(20+14 * sqrt(2)) * Gamma(5/4)^6) / Pi^(9/2).

%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.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Empirical: Equals Sum_{k>=0} A136028(k) / exp(k*Pi).

%e 1.2967852853151984329303931791739204694...

%t First[RealDigits[(64*Sqrt[20 + 14*Sqrt[2]]*Gamma[5/4]^6)/Pi^(9/2), 10, 100]]

%o (PARI) -(1/64) * gamma(5/8)^6 * (7 * sqrt(2)+10) * sqrt(2) * (2+2^(1/2))^(1/2) / Pi^(3/2) / gamma(7/8)^6 / (2^(1/2)-2)

%Y Cf. A136028.

%K nonn,cons

%O 1,2

%A _Simon Plouffe_, Sep 18 2025