A393259 - OEIS

%I #7 Feb 09 2026 18:41:26

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

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

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

%N Decimal expansion of 5*Pi^2/54 - 197/216.

%D Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See exercise 111 at page 269.

%H Michael I. Shamos, <a href="https://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 24.

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

%F Equals Sum_{k>=0} (k!/(4 + k)!)^2 [Knopp].

%F Equals Sum_{k>0} 1/(k*(k + 1)*(k + 2)*(k + 3))^2 [Shamos].

%e 0.001815222323088761003193611099643623640157352522...

%t Join[{0,0},RealDigits[5Pi^2/54-197/216,10,100][[1]]]

%Y Cf. A002388, A102753, A145426, A145427.

%K nonn,cons,easy

%O 0,4

%A _Stefano Spezia_, Feb 07 2026