🔢 Catalan Numbers — Structures, One by One (2D)
Enumerate the objects Cₙ actually counts, not just the number
Interpretation
Balanced parentheses
Binary trees
Lattice paths
n =
3
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Cₙ =
5
Structure
1
/
5
Step-through mode
C₃ = (2·3)! / ((3+1)!·3!) = 5