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A019775 Decimal expansion of sqrt(e)/2.

%I A019775 #21 Jul 08 2025 07:39:07
%S A019775 8,2,4,3,6,0,6,3,5,3,5,0,0,6,4,0,7,3,4,2,4,3,2,5,3,9,3,9,0,7,0,8,1,7,
%T A019775 8,5,8,2,6,8,8,8,0,5,0,3,5,5,0,7,4,0,0,5,7,8,7,5,3,9,6,5,5,8,2,0,3,3,
%U A019775 0,5,1,0,5,9,7,1,0,7,8,0,4,3,1,6,3,8,8,2,6,0,0,2,8,1,8,3,3,2,1
%N A019775 Decimal expansion of sqrt(e)/2.
%H A019775 Ivan Panchenko, <a href="/A019775/b019775.txt">Table of n, a(n) for n = 0..1000</a>
%H A019775 Pratchayaporn Doemlim, Vichian Laohakoso and Janyarak Tongsomporn, <a href="https://doi.org/10.48048/wjst.2019.6956">The Continued Fractions of Certain Exponentials</a>, Walailak Journal of Science and Technology, Vol. 16, No. 09, Sept. 2019, pp. 615 - 624.
%F A019775 From _Amiram Eldar_, Jul 21 2020: (Start)
%F A019775 Equals Sum_{k>=0} 1/(2^(k+1)*k!).
%F A019775 Equals Sum_{k>=0} 1/(2^k*(k-1)!).
%F A019775 Equals Sum_{k>=0} k/(2*k)!!.
%F A019775 Equals A019774/2. (End)
%F A019775 From _Peter Bala_, Jun 29 2024: (Start)
%F A019775 Equals Sum_{n >= 0} 1/((1 - 4*n^2)*(2^n)*n!).
%F A019775 Continued fraction expansion [0; 1, 4, 1, 2, 3, 1, 4, 3, 1, ..., 2*n, 3, 1, ...]. (End)
%e A019775 0.82436063535006407342432539390708178582688805035507...
%t A019775 RealDigits[Sqrt[E]/2,10,120][[1]] (* _Harvey P. Dale_, Jun 18 2014 *)
%Y A019775 Cf. A019774.
%K A019775 nonn,cons
%O A019775 0,1
%A A019775 _N. J. A. Sloane_