• 호남수학학술지
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• 제38권2호
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• pp.279-294
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• 2016

Half integer values of harmonic numbers and reciprocal binomial squared coeffients sums are investigated in this paper. Closed form representations and integral expressions are developed for the infiite series.

• 대한수학회논문집
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• 제29권2호
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• pp.239-255
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• 2014

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

• 대한수학회보
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• 제56권3호
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• pp.649-658
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• 2019

In this paper, we prove some congruences involving the generalized Catalan numbers and harmonic numbers modulo $p^2$, one of which is $$\sum\limits_{k=1}^{p-1}k^2B_{p,k}B_{p,k-d}{\equiv}4(-1)^d\{{\frac{1}{3}}d(2d^2+1)(4pH_d-1)-p\({\frac{26}{9}}d^3+{\frac{4}{3}}d^2+{\frac{7}{9}}d+{\frac{1}{2}}\)\}\;(mod\;p^2)$$, where a prime number p > 3 and $1{\leq}d{\leq}p$.

• 호남수학학술지
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• 제35권3호
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• pp.373-379
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• 2013

In contrast with numerous identities involving the binomial coefficients and the Stirling numbers of the first and second kinds, a few identities involving the Eulerian numbers have been known. The objective of this note is to present certain interesting and (presumably) new identities involving the Eulerian numbers by mainly making use of Worpitzky's identity.

• 대한수학회보
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• 제58권5호
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• pp.1079-1095
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• 2021

In this paper, we give new congruences with the generalized Catalan numbers and harmonic numbers modulo p². One of our results is as follows: for prime number p > 3, $${\sum\limits_{k=(p+1)/2}^{p-1}}\;k^2B_{p,k}B_{p,k-(p-1)/2}H_k{\equiv}(-1)^{(p-1)/2}\(-{\frac{521}{36}}p-{\frac{1}{p}}-{\frac{41}{12}}+pH^2_{3(p-1)/2}-10pq^2_p(2)+4\({\frac{10}{3}}p+1\)q_p(2)\)\;(mod\;p^2),$$ where q_p(2) is Fermat quotient.