Super congruences for two Apery-like sequences

被引：12

作者：

Sun, Zhi-Hong ^{[1
]}

机构：

[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2018年 / 24卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Apery-like number; congruence; binomial coefficients; Euler number; binary quadratic form; LEGENDRE POLYNOMIALS; BERNOULLI NUMBERS; SUPERCONGRUENCES; IDENTITIES; ANALOGS; SERIES; SUMS;

D O I：

10.1080/10236198.2018.1515930

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For n = 0, 1, 2,... let Tn = Sigma nk = 0 Sigma nk Sigma 2 Sigma 2k n Sigma 2 and Sn = Sigma nk = 0 Sigma nk Sigma Sigma 2k k = Sigma 2n-2k n-k =. Then {Tn} and {Sn} are Apery-like numbers. In this paper we obtain some congruences and pose several challenging conjectures for sums involving {T-n} or {S-n}.

引用

页码：1685 / 1713

页数：29

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