A supercongruence for generalized Domb numbers

Abstract

Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier's seven "sporadic" solutions to second order Apery-like differential equations.

7 pages, to appear in Funct. Approx. Comment. Math

References in corpus (6)

• Ramanujan-type supercongruences
• Elliptic integral evaluations of Bessel moments
• Extending Gaussian hypergeometric series to the $p$-adic setting
• Supercongruences for Apery-like numbers
• Congruences via modular forms
• Supercongruences satisfied by coefficients of 2F1 hypergeometric series

Cited by in corpus (9)

• Supercongruences for sporadic sequences
• q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
• Multivariate Apéry numbers and supercongruences of rational functions
• New representations for all sporadic Apéry-like sequences, with applications to congruences
• Sequences, modular forms and cellular integrals
• Congruences for Catalan-Larcombe-French numbers
• Divisibility properties of sporadic Apéry-like numbers
• Rational 2-functions are abelian
• On sporadic sequences