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Using a combinatorial approach, we introduce the t -successive associated Stirling numbers and we give the recurrence relation and the generating function. We also establish the unimodality of sequence { n−2k k } k lying over a ray of the second kind’s Stirling triangle. Some combinatorial identities are given.

The $t$-successive associated Stirling numbers, $t$-Fibonacci--Stirling numbers, and unimodality