Geodesic
Linear recurrence relations for sums of products of two terms
The electronic journal of combinatorics, Tome 18 (2011) no. 1

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Zbl
For a sum of the form $\sum_k F({\boldsymbol n},k)G({\boldsymbol n},k)$, we set up two systems of equations involving shifts of $F({\boldsymbol n},k)$ and $G({\boldsymbol n},k)$. Then we solve the systems by utilizing the recursion of $F({\boldsymbol n},k)$ and the method of undetermined coefficients. From the solutions, we derive linear recurrence relations for the sum. With this method, we prove many identities involving Bernoulli numbers and Stirling numbers.
DOI : 10.37236/657
Classification : 68W30, 33F10, 05A19
Mots-clés : symbolic summation, Stirling numbers, Bernoulli numbers, coupled difference equations 
Yan-Ping Mu. Linear recurrence relations for sums of products of two terms. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/657
@article{10_37236_657,
     author = {Yan-Ping Mu},
     title = {Linear recurrence relations for sums of products of two terms},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/657},
     zbl = {1257.68150},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/657/}
}
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