We calculate the Hankel determinants of sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries' natural and deep connection with Bernoulli polynomials, a special case of the matrix can be constructed from a corresponding Vandermonde matrix. As a result, instead of asymptotic analysis, we give a direct proof of calculating an entry of its inverse.

翻译：我们计算出伯努利多元动物序列的汉克尔决定因素。 这个相应的汉克尔矩阵来自对非参数回归差异的统计估计。 除了其条目与伯努利多元动物的自然和深层联系外,还可以用相应的范德蒙德矩阵构建一个特例。 因此,我们没有进行无药可依的分析,而是给出一个直接的证据来计算其反向输入。