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Decimal expansion of probability that a random walk on a 4-d lattice returns to the origin.
13

%I #30 Jul 02 2022 15:01:26

%S 1,9,3,2,0,1,6,7,3,2,2,4,9,8,3,9,3,7,3,4,1,8,7,0,9,7,3,3,2,9,3,6,9,1,

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

%U 2,2,9,2,4,9,5,8,1,0,8,4,6,0,2,9,4,4,3

%N Decimal expansion of probability that a random walk on a 4-d lattice returns to the origin.

%H Marc Mezzarobba, <a href="/A086232/b086232.txt">Table of n, a(n) for n = 0..9999</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolyasRandomWalkConstants.html">PĆ³lya's Random Walk Constants</a>.

%F Equals 1 - 1/A242812. - _Amiram Eldar_, Aug 28 2020

%e 0.1932016...

%t First[RealDigits[1 - 1/NIntegrate[BesselI[0, t/4]^4 * Exp[ -t], {t, 0, Infinity}, PrecisionGoal->50, WorkingPrecision->350]]] (* _Ryan Propper_, Jul 12 2005 *)

%Y Cf. A086230, A086233, A086234, A086235, A086236, A242812.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Jul 12 2003

%E More terms from _Ryan Propper_, Jul 12 2005

%E a(51) corrected and more terms using the data at A242812 added by _Amiram Eldar_, Aug 28 2020