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A258619 Decimal expansion of Sum_{k>=0} (1/A055209(k)).

%I A258619 #23 Sep 08 2022 08:46:12
%S A258619 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 A258619 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 A258619 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 A258619 Decimal expansion of Sum_{k>=0} (1/A055209(k)).
%H A258619 G. C. Greubel, <a href="/A258619/b258619.txt">Table of n, a(n) for n = 1..5000</a>
%e A258619 2.2569565016088514950284576370776548515676635143755759249....
%t A258619 RealDigits[Sum[1/BarnesG[k + 2]^2, {k, 0, 80}], 10, 100][[1]] (* _G. C. Greubel_, Nov 28 2018 *)
%o A258619 (Sage)
%o A258619 def A055209(n) :
%o A258619    return prod(factorial(i)^(2) for i in (0..n))
%o A258619 N(sum(1/A055209(n) for n in (0..12)), digits=105)
%o A258619 (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 A258619 (PARI) default(realprecision, 100); sum(n=0,50, 1.0/prod(i=0, n, i!)^2) \\ _G. C. Greubel_, Nov 28 2018
%Y A258619 Cf. A055209.
%K A258619 nonn,cons
%O A258619 1,1
%A A258619 _Jani Melik_, Jun 06 2015
%E A258619 Name corrected by _Amiram Eldar_, Nov 17 2020