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

Authors: HACENE BELBACHIR, ASSIA-FETTOUMA TEBTOUB

Abstract: Using a combinatorial approach, we introduce the \textit{$t$-successive associated Stirling numbers} and we give the recurrence relation and the generating function. We also establish the unimodality of sequence $\genfrac{\{}{\}}{0pt}{}{n-2k}{k}_{k}$ lying over a ray of the second kind's Stirling triangle. Some combinatorial identities are given.

Keywords: $t$-Successive associated Stirling numbers, recurrence relations, generating function, log-concavity, unimodality,

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