A248791 - OEIS

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A248791

Decimal expansion of P_2(xi), the maximum limiting probability that a random n-permutation has exactly two cycles exceeding a given length.

0

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..100.

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

-Pi^2/12 + (1/2)*log(1 + sqrt(e))^2 + Li_2(1/(1 + sqrt(e))).

EXAMPLE

0.0727887386608213733667186633181914296889295494487...

MATHEMATICA

xi = 1/(1 + Sqrt[E]); P2[x_] := -Pi^2/12 + (1/2)*Log[x]^2 + PolyLog[2, x]; Join[{0}, RealDigits[P2[xi], 10, 100] // First]

PROG

(Python)

from mpmath import *

mp.dps=101

xi=1/(1 + sqrt(e))

C = -pi**2/12 + (1/2)*log(xi)**2 + polylog(2, xi)

print([int(n) for n in list(str(C)[2:-1])]) # Indranil Ghosh, Jul 03 2017

CROSSREFS

Cf. A143301, A246849, A248080.

Sequence in context: A301864 A295421 A217172 * A253383 A010506 A197845

Adjacent sequences: A248788 A248789 A248790 * A248792 A248793 A248794

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Oct 14 2014

STATUS

approved