The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A248080 Decimal expansion of P_0(xi), the maximum limiting probability that a random n-permutation has no cycle exceeding a given length. 1
 0, 9, 8, 7, 1, 1, 7, 5, 4, 4, 8, 0, 7, 1, 4, 6, 9, 2, 4, 9, 3, 7, 2, 1, 3, 0, 8, 2, 3, 7, 0, 2, 0, 6, 7, 9, 9, 3, 3, 3, 3, 3, 3, 5, 4, 7, 8, 0, 8, 4, 4, 0, 0, 0, 2, 5, 6, 6, 9, 7, 9, 0, 8, 3, 6, 2, 2, 5, 2, 5, 3, 6, 4, 2, 7, 4, 0, 6, 3, 0, 1, 5, 8, 6, 2, 6, 3, 0, 0, 2, 1, 5, 7, 5, 9, 2, 4, 5, 4, 6, 1, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..101. Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 29. Michael Lugo, The number of cycles of specified normalized length in permutations, arXiv:0909.2909 [math.CO], 2009. FORMULA (1/2)*log(1 + sqrt(e))^2 - log(1 + sqrt(e)) + Li_2(1/(1 + sqrt(e))) - Pi^2/12 + 1. EXAMPLE 0.098711754480714692493721308237020679933333354780844... MATHEMATICA xi = 1/(1 + Sqrt[E]); P0[x_] := Log[x]^2/2 + Log[x] + PolyLog[2, x] - Pi^2/12 + 1; Join[{0}, RealDigits[P0[xi], 10, 101] // First] PROG (Python) from mpmath import * mp.dps=102 xi=1/(1 + sqrt(e)) C = log(xi)**2/2 + log(xi) + polylog(2, xi) - pi**2/12 + 1 print([int(n) for n in list(str(C)[2:-1])]) # Indranil Ghosh, Jul 04 2017 CROSSREFS Cf. A143301, A246849. Sequence in context: A129269 A094145 A002388 * A278828 A334448 A011116 Adjacent sequences: A248077 A248078 A248079 * A248081 A248082 A248083 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Oct 14 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 13:56 EDT 2024. Contains 372826 sequences. (Running on oeis4.)