Questions tagged [sequences-and-series]

For questions concerning sequences and series. Typical questions concern, but are not limited to: recurrence relations, convergence tests, identifying sequences, identifying terms. For questions on finite sums, use the (summation) tag instead.

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How to prove all $c_{n},d_{n}$ to be integers if $(n+1)c_{n}=nc_{n-1}+2nd_{n-1}$ and $d_{n}=2c_{n-1}+d_{n-1}$?

Let sequences $(c_n)$ and $(d_n)$ be given by $$c_0=0,\:d_0=1$$ and recursively for $n\ge 1$ by $$\begin{align} c_n & =\frac{n}{n+1}c_{n-1}+\frac{2n}{n+1}d_{n-1} \\[2ex] d_n & =2c_{n-1}+d_{n-1}...