OFFSET
0,1
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Pratchayaporn Doemlim, Vichian Laohakoso and Janyarak Tongsomporn, The Continued Fractions of Certain Exponentials, Walailak Journal of Science and Technology, Vol. 16, No. 09, Sept. 2019, pp. 615 - 624.
FORMULA
From Amiram Eldar, Jul 21 2020: (Start)
Equals Sum_{k>=0} 1/(2^(k+1)*k!).
Equals Sum_{k>=0} 1/(2^k*(k-1)!).
Equals Sum_{k>=0} k/(2*k)!!.
Equals A019774/2. (End)
From Peter Bala, Jun 29 2024: (Start)
Equals Sum_{n >= 0} 1/((1 - 4*n^2)*(2^n)*n!).
Continued fraction expansion [0; 1, 4, 1, 2, 3, 1, 4, 3, 1, ..., 2*n, 3, 1, ...]. (End)
EXAMPLE
0.82436063535006407342432539390708178582688805035507...
MATHEMATICA
RealDigits[Sqrt[E]/2, 10, 120][[1]] (* Harvey P. Dale, Jun 18 2014 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved