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Hankel determinants of sequences related to Bernoulli and Euler numbers havebeen studied before, and numerous identities are known. However, when asequence is shifted by one unit, the situation often changes significantly. Inthis paper we use classical orthogonal polynomials and related methods to provea general result concerning Hankel determinants for shifted sequences. We thenapply this result to obtain new Hankel determinant evaluations for a total of$13$ sequences related to Bernoulli and Euler numbers, one of which concernsEuler polynomials.

Hankel Determinants of shifted sequences of Bernoulli and Euler numbers