Geodesic
Asymptotic normality of the Stirling-Whitney-Riordan triangle
Filomat, Tome 37 (2023) no. 9, p. 2923

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DOI

Recently, Zhu [34] introduced a Stirling-Whitney-Riordan triangle [T n,k ] n,k≥0 satisfying the recurrence T n,k = (b 1 k + b 2)T n−1,k−1 + [(2λb 1 + a 1)k + a 2 + λ(b 1 + b 2)]T n−1,k + λ(a 1 + λb 1)(k + 1)T n−1,k+1 , where initial conditions T n,k = 0 unless 0 ≤ k ≤ n and T 0,0 = 1. Denote by T n = n k=0 T n,k. In this paper, we show the asymptotic normality of T n,k and give an asymptotic formula of T n. As applications, we show the asymptotic normality of many famous combinatorial numbers, such as the Stirling numbers of the second kind, the Whitney numbers of the second kind, the r-Stirling numbers and the r-Whitney numbers of the second kind.
DOI : 10.2298/FIL2309923G
Classification : 05A16, 05A15, 11B73
Keywords: Asymptotic normality, Asymptotic formula, Stirling-Whitney-Riordan triangle 
Wan-Ming Guo; Lily Li Liu. Asymptotic normality of the Stirling-Whitney-Riordan triangle. Filomat, Tome 37 (2023) no. 9, p. 2923 . doi: 10.2298/FIL2309923G
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     author = {Wan-Ming Guo and Lily Li Liu},
     title = {Asymptotic normality of the {Stirling-Whitney-Riordan} triangle},
     journal = {Filomat},
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     year = {2023},
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     doi = {10.2298/FIL2309923G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2309923G/}
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