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}.
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页码：1685 / 1713
页数：29
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