We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps E = (1, 0), D = (1, 1), N = (0, 1), and D ′ = (1, 2) and not going above the line y = x . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition, we find some new interesting identities.

中文翻译：

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格路径枚举产生的广义 Schröder 矩阵

我们从 Riordan 阵列中引入了一组新的广义 Schröder 矩阵，这些矩阵是通过对步长 E = (1, 0)、D = (1, 1)、N = (0, 1) 和D ′ = (1, 2) 并且不超过线 y = x 。我们还考虑了广义 Delannoy 矩阵的一半，它是从这些晶格路径的枚举中推导出来的，没有限制。考虑这些矩阵之间的相关性。作为说明，我们给出了几个具有组合兴趣的 Riordan 数组的例子。此外，我们还发现了一些新的有趣的身份。