The Economically Impossible Optimum Faring (solved ?)

In an article in 2013, we've seen that the number of combinations is huge, but having a closer look, the number of pricing isn't that huge.

Number of flight(s) (legs) or Origin Destinations	number of combination(s)	Number of pricing(s) required
1	1	1
2	2	3
3	5	7
4	15	15
5	52	31
6	203	63
7	877	127
8	4'140	255
9	21'147	511
10	115'975	1'023
11	678'570	2'047
12	4'213'597	4'095
13	27'644'437	8'191
14	190'899'322	16'383
15	1'382'958'545	32'767

maybe it could open the door to something ?

code

Function pricingrequired(nombre As Integer) As Long

Dim i As Integer

i = 0

If nombre <= 1 Then

pricingrequired = 1

Else

For i = 1 To nombre Step 1

pricingrequired = pricingrequired + WorksheetFunction.Fact(nombre) / (WorksheetFunction.Fact(i) * WorksheetFunction.Fact(nombre - i))

Next i

End If

End Function