A generalization of a binomial sum for the Stirling numbers of the second kind
A generalization of a binomial sum for the Stirling numbers of the second kind
A combinatorial sum for the Stirling numbers of the second kind is generalized. This generalization provides us with a new explicit formula for the binomial sum ∑k=0 n=krak(k n where a, b ∈ ℝ- {0}, n, r ∈ ℕ. As relevant special cases, simple explicit expressions for both the binomial sum ∑k=0 n kr(k n) and the raw moment of order r of the binomial distribution B (n, p) are given. All these sums are expressed in terms of generalized r-permutations.
0,239
0,265
SCIE
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305
Q4
Combinatorial identity, Generalized r-permutations, Bell and Stirling numbers, Generalized sampling, Stirling numbers of the second kind, combinatorial identity, generalized sampling, generalized \(r\)-permutations, binomial moments, 240401 Bioestadística, Binomial moments, Combinatorial identities, bijective combinatorics, 120903 Análisis de datos
Combinatorial identity, Generalized r-permutations, Bell and Stirling numbers, Generalized sampling, Stirling numbers of the second kind, combinatorial identity, generalized sampling, generalized \(r\)-permutations, binomial moments, 240401 Bioestadística, Binomial moments, Combinatorial identities, bijective combinatorics, 120903 Análisis de datos
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