On a combinatorial problem of Asmus Schmidt

Details On a combinatorial problem of Asmus Schmidt On a combinatorial problem of Asmus Schmidt

2003-11-12

arxiv.org/abs/math/0311195v1

Electron. J. Combin. 11:1 (2004), #R22, 8 pages

Mathematics

Classical Analysis and ODEs

7 pages, AmSTeX

Scientific paper

For any integer $r\ge2$, define a sequence of numbers
$\{c_k^{(r)}\}_{k=0}^\infty$, independent of the parameter $n$, by $$
\sum_{k=0}^n{\binom nk}^r{\binom{n+k}k}^r =\sum_{k=0}^n\binom
nk\binom{n+k}kc_k^{(r)}, \qquad n=0,1,2,...c. $$ We prove that all the numbers
$c_k^{(r)}$ are integers.

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