A099935 Decimal expansion of Sum_{k>=0} (-1)^(k+1)*A000045(k)/k!.

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

Offset: 0

Author

Benoit Cloitre, Nov 12 2004

Keywords

• cons
• nonn

Comments

This number is the coefficient of x in the reduction of e^(-x) by the substitution x^2->x+1; see A193026 and A193010.

Examples

			0.74102792152357735584178398667102441173255884250150...
		

Crossrefs

Cf. A000045, A001113, A098689, A193010, A193026.

Programs

Mathematica

(E^(1+2/GoldenRatio)-1) / (E^GoldenRatio*(2*GoldenRatio-1)) // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 13 2013 *)

PARI

exp(-1/2)*(2/sqrt(5))*sinh(sqrt(5)/2) \\ Michel Marcus, Feb 07 2022

Formula

Equals exp(-1/2)*(2/sqrt(5))*sinh(sqrt(5)/2).

Equals A098689 / e. - Amiram Eldar, Feb 07 2022