Some Inverse Relations Determined by Catalan Matrices
Some Inverse Relations Determined by Catalan Matrices
We use the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:math>-sequence and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>Z</mml:mi></mml:mrow></mml:math>-sequence of Riordan array to characterize the inverse relation associated with the Riordan array. We apply this result to prove some combinatorial identities involving Catalan matrices and binomial coefficients. Some matrix identities obtained by Shapiro and Radoux are all special cases …