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\iteman{io-port 05723741}
\itemau{Mattarei, Sandro; Tauraso, Roberto}
\itemti{Congruences of multiple sums involving sequences invariant under the binomial transform.}
\itemso{J. Integer Seq. 13, No. 5, Article ID 10.5.1, 12 p., electronic only (2010).}
\itemab
The authors present several congruences of multiple harmonic sums with coefficients involving the invariant sequences contained in the $eigenspaces$, related to the $eigenvalues$ of the binomial inversion formula $$T(\{a_n\})=\left\{\sum_{k=0}^{n} {n\choose k}(-1)^{k} a_{k}\right\},$$ whose properties were analyzed by {\it Z.-H. Sun} [(*) Fibonacci Q. 39, No. 4, 324--333 (2001; Zbl 0987.05013)] and by {\it Y. Wang} [Fibonacci Q. 43, No. 1, 46--52 (2005; Zbl 1073.05010)]. Based also on contributions from {\it Z.-H. Sun} [Discrete Math. 308, No. 1, 71--112 (2008; Zbl 1138.11006)] and from {\it X. Zhou} and {\it T. Cai} [Proc. Am. Math. Soc. 135, No. 5, 1329--1333 (2007; Zbl 1115.11006)], the original theorem-proving developed by the present authors confirms many previous results found by {\it Z.-H. Sun} (*) and by {\it L.-L. Zhao} and {\it Z.-W. Sun} [J. Number Theory 130, No. 4, 930--935 (2010; Zbl 1185.11007)]. Beyond innovative strategies achieving old results, the papers offers new proofs such as a polynomial congruence which reduces the evaluation modulo $p$ of multiple harmonic sums to certain single sums, a pair of congruences involving Bernoulli numbers and another matching pair of congruences with the parity of $n$ reversed. These congruences both refine (modulo $p^2$) and complement (covering the case where $n$ has the opposite parity) the congruences proved by L. Zhao and Z. Sun (loc. cit).
\itemrv{Enzo Bonacci (Latina)}
\itemcc{}
\itemut{binomial transform; multiple sum; congruence; Bernoulli polynomial}
\itemli{emis:journals/JIS/VOL13/Tauraso/tauraso22.html}
\end