A243266 Decimal expansion of a parking constant related to the asymptotic expected number of cars, assuming random car lengths.

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

Offset: 0

Author

Jean-François Alcover, Jun 02 2014

Keywords

• nonn
• cons

Examples

			0.9848712825259953044727952215...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Renyi's parking constant, p. 279.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Eric Weisstein's MathWorld, Rényi's Parking Constants

Crossrefs

Cf. A050996.

Programs

Mathematica

(1-1/2^((Sqrt[17]-1)/4))*Sqrt[Pi]*Gamma[Sqrt[17]/2]/(Gamma[(Sqrt[17]+1)/4]*Gamma[(Sqrt[17]+3)/4]^2) // RealDigits[#, 10, 100]& // First

PARI

(1-1/2^((sqrt(17)-1)/4))*sqrt(Pi)*gamma(sqrt(17)/2)/(gamma((sqrt(17)+1)/4)*gamma((sqrt(17)+3)/4)^2) \\ G. C. Greubel, Feb 14 2017

Formula

(1-1/2^((sqrt(17)-1)/4))*sqrt(Pi)*GAMMA(sqrt(17)/2)/(GAMMA((sqrt(17)+1)/4)*GAMMA((sqrt(17)+3)/4)^2), where GAMMA is the Euler Gamma function.