A258619 - OEIS

%I #23 Sep 08 2022 08:46:12

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

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

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

%N Decimal expansion of Sum_{k>=0} (1/A055209(k)).

%H G. C. Greubel, <a href="/A258619/b258619.txt">Table of n, a(n) for n = 1..5000</a>

%e 2.2569565016088514950284576370776548515676635143755759249....

%t RealDigits[Sum[1/BarnesG[k + 2]^2, {k, 0, 80}], 10, 100][[1]] (* _G. C. Greubel_, Nov 28 2018 *)

%o (Sage)

%o def A055209(n) :

%o    return prod(factorial(i)^(2) for i in (0..n))

%o N(sum(1/A055209(n) for n in (0..12)), digits=105)

%o (Magma) SetDefaultRealField(RealField(100)); b:=[1] cat [(&*[(Factorial(k))^2: k in [1..n]]): n in [1..60]];  (&+[1.0/b[k]: k in [1..50]]); // _G. C. Greubel_, Nov 28 2018

%o (PARI) default(realprecision, 100); sum(n=0,50, 1.0/prod(i=0, n, i!)^2) \\ _G. C. Greubel_, Nov 28 2018

%Y Cf. A055209.

%K nonn,cons

%O 1,1

%A _Jani Melik_, Jun 06 2015

%E Name corrected by _Amiram Eldar_, Nov 17 2020