Some congruences on harmonic numbers and binomial sums
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DOI: 10.1007/s10998-016-0155-y
Abstract: Some new congruences on harmonic numbers are established. In addition, we obtain a congruence of binomial sums, which is a generalization of that of van Hamme and confirms a conjecture of Swisher. read more here.
Keywords: congruences harmonic; binomial sums; harmonic numbers; numbers binomial ... See more keywords
On two supercongruences of double binomial sums
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DOI: 10.1007/s10998-020-00377-4
Abstract: In this note we confirm two conjectural supercongruences of double sums of binomial coefficients due to El Bachraoui. read more here.
Keywords: supercongruences double; two supercongruences; binomial sums; double binomial ... See more keywords
Binomial sums involving Catalan numbers
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DOI: 10.1216/rmj.2021.51.1221
Abstract: Recently, various interesting binomial sums involving Catalan numbers have been derived and computed. Inspired from them, several binomial sums involving Catalan numbers are evaluated in closed forms using a hypergeometric series approach. read more here.
Keywords: binomial sums; catalan numbers; involving catalan; sums involving ... See more keywords
Three binomial sums weighted by falling and rising factorials
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DOI: 10.3906/mat-1706-24
Abstract: In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial coefficients. Then… read more here.
Keywords: binomial sums; weighted falling; three binomial; falling rising ... See more keywords