I have here left out the indices of the elements for easier typing but hopefully this can still be understood.

Shift down the elements in matrix one step to get matrix .

Add a diagonal of ones to the main diagonal in matrix to get matrix .

Change the sign of all the elements below the main diagonal in matrix so that you get matrix .

Calculate the matrix inverse of matrix to get matrix

Iterate by replacing matrix with matrix .

Matrix should then converge to the Catalan numbers in all columns.

Keywords: Catalan numbers, INVERT transform, matrix inverse.

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