Abstract
The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.
Highlights
IntroductionFor any integer n ≥ 0, the Fubini polynomials { Fn (y)} are defined by the coefficients of the generating function
For any integer n ≥ 0, the Fubini polynomials { Fn (y)} are defined by the coefficients of the generating function ∞ Fn (y) n = ·t, ∑ t 1 − y ( e − 1) n! n =0 (1)
Fa1 (y) Fa2 (y) where the summation is over all k-tuples with non-negative integer coordinates ( a1, a2, · · ·, ak ) such that a1 + a2 + · · · + ak = n. It seems there is no valid method to solve the computational problem of (4). This problem is significant, it can reveal the structure of Fubini polynomials itself and its internal relations, at least it can reflect the combination properties of Fubini polynomials
Summary
For any integer n ≥ 0, the Fubini polynomials { Fn (y)} are defined by the coefficients of the generating function. These polynomials occupy indispensable positions in the theory and application of mathematics. Where the summation is over all k-tuples with non-negative integer coordinates ( a1 , a2 , · · · , ak ) such that a1 + a2 + · · · + ak = n About this content, it seems there is no valid method to solve the computational problem of (4). It seems there is no valid method to solve the computational problem of (4) This problem is significant, it can reveal the structure of Fubini polynomials itself and its internal relations, at least it can reflect the combination properties of Fubini polynomials.
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