Further identities on Catalan numbers

On the Catalan Numbers and Some of Their Identities

“…The main results of this paper are Theorem 1 and Theorem 2. They gave two special expressions for convolution (2). In addition, Corollary 1 gives a close relationship between C(h, i) and C h+i .…”

“…These numbers occupy a pivotal position in combinatorial mathematics, as many counting problems are closely related to Catalan numbers, and some famous examples can be found in R. P. Stanley [1]. Many papers related to the Catalan numbers and other special sequences can also be found in references [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], especially the works of T. Kim et al give a series of new identities for the Catalan numbers, see [9][10][11][12][13][14], these are important results in the related field.…”

Summation Formulas for Certain Combinatorial Sequences

“…By means of the numbers A α (n, k) and Lemma 1, we may establish more summation formulas. For example, recalling the Catalan numbers C n [14] defined by…”

A Note on the Sequence Related to Catalan Numbers

“…Some notes: If we replace C(h, i) ( D(h, i)) in Theorem 1 (Theorem 2) with the formula for C(h, i) (D(h, i)) in our Theorem 3 (Theorem 4), then we can get a more accurate representation for convolution sums (2).…”