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

0,1

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

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.

Example

0.9848712825259953044727952215...

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

Prog

(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

Crossrefs

Cf. A050996.

Sequence in context: A019720 A200117 A019889 * A358659 A010548 A011458

Adjacent sequences: A243263 A243264 A243265 * A243267 A243268 A243269

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 02 2014

Status

approved