Lengyel's Constant

Author

Eric W. Weisstein
May 20, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/LengyelsConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/LengyelsConstant.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Value

Λ=1.0986858055`11

According to R.G. Wilson

1.09868580552518701

Recurrence

Sum[StirlingS2[n,k]Z[k],{k,n-1}]

Z[1]:=1
Z[n_]:=Z[n]=Sum[StirlingS2[n,k]Z[k],{k,n-1}]

Table[Z[n],{n,10}]

Sum[StirlingS2[n,k]Z[k],{k,n-1}]

Limit

r[n_]:=((Z[n](((2Log[2]))^n)(n^(1+Log[2]/3)))/(((n!))^2))

N[r[1000],20]//Timing

N[r[1000],20]//Timing

SequenceLimit[N[Array[r,1000],50]]//Timing

SequenceLimit[N[Array[r,1000],100]]//Timing

SequenceLimit[N[Array[r,1000],500]]//Timing

ListPlot[Table[r[n],{n,1000}],Joined->True,PlotStyle->Red]