A098689 Decimal expansion of Sum_{n>=0} Fibonacci(n)/n!.

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

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Oct 27 2004

Keywords

• cons
• nonn

Examples

			2.01432273345831573658134625546975913565911146958112...
		

Crossrefs

Cf. A000045, A001113, A099935.

Programs

Maple

with(combinat): evalf(sum(fibonacci(n)/n!, n=0..infinity), 120);

Mathematica

RealDigits[ Sum[ Fibonacci[n]/n!, {n, 0, 80}], 10, 105][[1]] (* Robert G. Wilson v, Nov 02 2004 *)
(E^GoldenRatio - E^(1-GoldenRatio))/(2*GoldenRatio-1) // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 13 2013 *)

PARI

sumpos(n=0, fibonacci(n)/n!) \\ Michel Marcus, Feb 07 2022

Formula

Equals (2/sqrt(5))*exp(1/2)*sinh(sqrt(5)/2). - Vladeta Jovovic, Oct 30 2004

Equals e * A099935. - Amiram Eldar, Feb 07 2022

Extensions

More terms from Robert G. Wilson v, Nov 02 2004