A374677 - OEIS

%I #15 Jul 17 2024 13:29:27

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

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

%U 9,1,6,1,7,1,8,5,2,0,9,6,4,0,4,8,0,1,5,4,9,8

%N Decimal expansion of (5/96)*Pi^2 - (log(2)^2)/8.

%H Paolo Xausa, <a href="/A374677/b374677.txt">Table of n, a(n) for n = 0..10000</a>

%H David Bailey, Peter Borwein, and Simon Plouffe, <a href="https://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf">On the Rapid Computation of Various Polylogarithmic Constants</a>, Mathematics of Computation, Vol. 66, No. 218, April 1997, pp. 903-913.

%F Equals A096615 - A253191/8.

%F Equals Sum_{k >= 1} d(k)/(2^floor((k + 1)/2)*k^2), where d is the periodic sequence {1, 0, -1, -1, -1, 0, 1, 1}. See Bailey et al. (1997), eq. 2.15, p. 907.

%e 0.4539852691502955833142419237860497501646027251778...

%t First[RealDigits[5*Pi^2/96 - Log[2]^2/8, 10, 100]]

%Y Cf. A096615, A253191, A367053.

%K nonn,cons

%O 0,1

%A _Paolo Xausa_, Jul 16 2024