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... (1.3) as well as Jacobi-type and Thron-type (defined in (1.7),(1.8)). The ordinary generating functions of our integer sequences have S-fractions with coefficients α 2k−1 = α 2k = k for factorials [Eul60, section 21], α 2k−1 = k 2 and α 2k = k(k +1) for the Genocchi numbers [Vie81, eq. A systematic study of some combinatorial families whose associated S-fraction coefficients (α n ) n⩾0 grow linearly in n was carried out by Sokal and Zeng in [SZ22]. ...
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