In[]:=
BellB[100]
Out[]=
47585391276764833658790768841387207826363669686825611466616334637559114497892442622672724044217756306953557882560751
BellB
In[]:=
DiscreteAsymptotic[BellB[n],{n,Infinity,1}]
Out[]=
-1-n+
n
ProductLog[n]

1
2
+n
n
ProductLog[n]
n
In[]:=
AsymptoticGreater[BellB[n],n^n,n->Infinity]
Out[]=
AsymptoticGreater[BellB[n],
n
n
,n∞]
In[]:=
AsymptoticGreater[BellB[n],Exp[n],n->Infinity]
Out[]=
AsymptoticGreater[BellB[n],
n

,n∞]
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/(n^n)],{n,100}]]]
Out[]=
20
40
60
80
100
-80
-60
-40
-20
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/(2^n)],{n,100}]]]
Out[]=
20
40
60
80
100
20
40
60
80
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/(3^n)],{n,100}]]]
Out[]=
20
40
60
80
100
10
20
30
40
50
60
70
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/((Log[n])^n)],{n,100}]]]
Power
:Infinite expression
1
0
encountered.
Out[]=
20
40
60
80
100
10
20
30
40
50
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/((Log[n]^2)^n)],{n,100}]]]
Power
:Infinite expression
1
0
encountered.
Out[]=
20
40
60
80
100
-15
-10
-5
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/((Log[n]^1.8)^n)],{n,100}]]]
Power
:Infinite expression
1
0.
encountered.
Out[]=
20
40
60
80
100
-6
-5
-4
-3
-2
-1
1
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/((Log[n]^1.7)^n)],{n,100}]]]
Power
:Infinite expression
1
0.
encountered.
Out[]=
20
40
60
80
100
-3
-2
-1
1
2
3
In[]:=
N[Sqrt[3]]
Out[]=
1.73205
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/((Log[n]^Sqrt[3])^n)],{n,100}]]]
Power
:Infinite expression
1
0
encountered.
Out[]=
20
40
60
80
100
-4
-3
-2
-1
1
In[]:=
ListLinePlot[Log10[Table[N[BellB[n]/((Log[n]^1.5)^n)],{n,100}]]]
Power
:Infinite expression
1
0.
encountered.
Out[]=
20
40
60
80
100
5
10
15