Some Inversion Formulas and Formulas for Stirling Numbers
نویسندگان
چکیده
منابع مشابه
Some Inversion Formulas and Formulas for Stirling Numbers
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
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Extensions of the Stirling numbers of the second kind and Dobinski-like formulas are proposed in a series of exercises for graduetes. Some of these new formulas recently discovered by me are to be found in A.K.Kwaśniewski’s source paper [1]. These extensions naturally encompass the well known q-extensions.The indicatory references are to point at a part of the vast domain of the foundations of ...
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and Applied Analysis 3 It follows from 1.11 or 1.12 that t n, k t n − 2, k − 2 − 1 4 n − 2 t n − 2, k , 1.13 and that t n, 0 δn,0 n ∈ N0 : N ∪ {0} , t n, n 1 n ∈ N , t n, k 0 n k odd , t n, k 0 k > n or k < 0 , 1.14 where δm,n denotes the Kronecker symbol. By 1.13 , we have t 2n 1, 1 −1 n 2n ! 42n ( 2n n ) , t 2n 2, 2 −1 n n! 2 n ∈ N0 , 1.15 t 2n 2, 4 −1 n 1 n! 2 ( 1 1 22 1 32 · · · 1 n2 ) n ∈ ...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2012
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-012-1155-1