On a combinatorial problem of Asmus Schmidt
The electronic journal of combinatorics, Tome 11 (2004) no. 1
For any integer $r\ge2$, define a sequence of numbers $\{c_k^{(r)}\}_{k=0,1,\dots}$, independent of the parameter $n$, by $$ \sum_{k=0}^n{n\choose k}^r{n+k\choose k}^r =\sum_{k=0}^n{n\choose k}{n+k\choose k}c_k^{(r)}, \qquad n=0,1,2,\dots. $$ We prove that all the numbers $c_k^{(r)}$ are integers.
@article{10_37236_1775,
author = {W. Zudilin},
title = {On a combinatorial problem of {Asmus} {Schmidt}},
journal = {The electronic journal of combinatorics},
year = {2004},
volume = {11},
number = {1},
doi = {10.37236/1775},
zbl = {1126.11012},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1775/}
}
W. Zudilin. On a combinatorial problem of Asmus Schmidt. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1775
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