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Constant term evaluation for summation of C-finite sequences

Abstract : Based on constant term evaluation, we present a new method to compute a closed form of the summation $∑_k=0^n-1 ∏_j=1^r F_j(a_jn+b_jk+c_j)$, where ${F_j(k)} are $C$-finite sequences and $a_j$ and $a_j+b_j$ are nonnegative integers. Our algorithm is much faster than that of Greene and Wilf.
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Qing-Hu Hou, Guoce Xin. Constant term evaluation for summation of C-finite sequences. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.761-772, ⟨10.46298/dmtcs.2806⟩. ⟨hal-01186231⟩

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