In this paper, we consider the recurrence properties of two generalized forms of Narayana’s cows sequence. On the one hand, we study Narayana’s cows sequence at negative indices and express it as the linear combination of the sequence at positive indices. On the other hand, we study the convolved Narayana number and obtain a computation formula for it.

中文翻译：

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Narayana奶牛序列的递归性质

在本文中，我们考虑了Narayana奶牛序列的两种广义形式的递归性质。一方面，我们研究负指数的Narayana牛序列，并将其表示为正指数的线性组合。另一方面，我们研究了卷积Narayana数，并为其求出了计算公式。