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On a combinatorial problem of Asmus Schmidt. (English) Zbl 1126.11012
Summary: For any integer $$r\geq 2$$, define a sequence of numbers $$\{c^{(r)}_k\}_{k=0,1,\dots}$$, independent of the parameter $$n$$, by $\sum^n_{k=0}\binom nk^r\binom{n+k}{k}^r=\sum^n_{k=0}\binom nk\binom{n+k}{k}c^{(r)}_k,\quad n=0,1,2,\dots.$ We prove that all the numbers $$c^{(r)}_k$$ are integers.

##### MSC:
 11B65 Binomial coefficients; factorials; $$q$$-identities 05A19 Combinatorial identities, bijective combinatorics
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