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Tables of the Generalized Stirling Numbers of the First Kind [PDF]
Journal of the ACM, 1964 The generalized Stirling numbers of the first kind are defined, certain of their basic properties are discussed, and tables are given for the square grid k = 0(1)10 and j = 0(1)10 with l = -10(1)10.
William F. Pickard
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On the p-adic valuation of stirling numbers of the first kind [PDF]
Acta Mathematica Hungarica, 2016 12 pages, 3 ...
LEONETTI, Paolo, SANNA, CARLO
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A note on degenerate Stirling numbers of the first kind
, 2018 12 ...
Taekyun Kim, Dae San Kim
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The 3-adic valuations of Stirling numbers of the first kind
, 2021 Let $n$ and $k$ be positive integers. The Stirling number of the first kind, denoted by $s(n,k)$, counts the number of permutations of $n$ elements with $k$ disjoint cycles. Let $p$ be a prime number and denote by $v_p(n)$ the $p$-adic valuation of $n$.
Min Qiu, Yulu Feng, Shaofang Hong
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A NOTE ON STIRLING NUMBERS OF FIRST KIND AND CYCLE TYPES OF A PERMUTATION
Revista Sergipana de Matemática e Educação MatemáticaThis paper proposes to establish a relationship between the Stirling numbers of the first kind and the cycle types of Sn, exhibiting the feasibility of a procedure to generate Stirling numbers of the first kind and proving some identities by the ...
Gabriel De Freitas Pinheiro +1 more
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Some identities on λ-analogues of r-Stirling numbers of the first kind
Filomat, 2020 In this paper, we study ?-analogues of the r-Stirling numbers of the first kind which have close connections with the r-Stirling numbers of the first kind and ?-Stirling numbers of the first kind.
Taekyun Kim, Dae San Kim
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On r-Stirling Type Numbers of the First Kind [PDF]
Turkish Journal of Analysis and Number Theory, 2019 Some combinatorial properties of -Stirling numbers are proved. Moreover, two asymptotic formulas for -Stirling numbers of the first kind derived using different methods are discussed and corresponding asymptotic formulas for the -Stirling type numbers of the first kind are obtained as corollaries.
Cristina B. Corcino, Roberto B. Corcino
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Moment Generating Stirling Numbers of the first kind and Applications
, 2023 In this paper we introduce and investigate moment generating Stirling numbers of the first kind, "`MSN1"'. They are inverses of MSN2's, which make the representation of the moments for a lot of statistical distributions in closed formulas possible. Both MSN1's and MSN2's are related to the r-Stirling numbers, and extend their properties to any real ...
Ludwig Frank
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On Non-central Stirling Numbers of the First Kind
, 2009 It is shown in this note that non-central Stirling numbers s(n,k,a) of the first kind naturally appear in the expansion of derivatives of the product of a power function and a logarithn function. We first obtain a recurrence relation for these numbers, and then, using Leibnitz rule we obtain an explicit formula for these numbers.
Milan Janjić
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The Extended Legendre-Stirling Numbers of the First Kind
DEStech Transactions on Engineering and Technology Research, 2016 The Legendre-Stirling numbers of the first kind j n Ps are defined by the coefficients of Taylor expansion of the function x(x 2)(x 6)(x (n 1)n) by Andrews and Littlejohn (see "A combinatorial interpretation of the Legendre-Stirling numbers", Proc. Amer. Math. Soc, 137: 2581-2590, 2009). In this paper, two new kinds of numbers jn Ps (n
Fangqing Wen +4 more
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