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Matching statistic: St000851
Mapping
St000851: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 4
['A',2]
 => 22
['B',2]
 => 28
['G',2]
 => 40
['A',3]
 => 140
['B',3]
 => 220
['C',3]
 => 220
['A',4]
 => 969
['B',4]
 => 1820
['C',4]
 => 1820
['D',4]
 => 1210
['F',4]
 => 2926
['A',5]
 => 7084
['B',5]
 => 15504
['C',5]
 => 15504
['D',5]
 => 10556
['A',6]
 => 53820
['B',6]
 => 134596
['C',6]
 => 134596
['D',6]
 => 93024
['E',6]
 => 119966
['A',7]
 => 420732
['B',7]
 => 1184040
['C',7]
 => 1184040
['D',7]
 => 826804
['E',7]
 => 1484032
['A',8]
 => 3362260
['B',8]
 => 10518300
['C',8]
 => 10518300
['D',8]
 => 7400250
['E',8]
 => 22309287
Description
The third Fuss-Catalan number of a finite Cartan type. The Fuss-Catalan numbers of a finite Cartan type are given by $$\frac{1}{|W|}\prod (d_i+mh) = \prod \frac{d_i+mh}{d_i}$$ where the products run over all degrees of homoneneous fundamenal invariants of the Weyl group of a Cartan type.