A019775 Decimal expansion of sqrt(e)/2.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			0.82436063535006407342432539390708178582688805035507...
		

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.

Crossrefs

Cf. A019774.

Programs

Mathematica

RealDigits[Sqrt[E]/2,10,120][[1]] (* Harvey P. Dale, Jun 18 2014 *)

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)