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## Main Question or Discussion Point

Consider a 2D variable coefficient linear recurrence relation. An example might be:

[tex]b_{n,j+1} (j+1)(2n-1)(2n-2) = (2n-2+j)(2n-1+j)b_{n-1,j}[/tex]

which has the solution

[tex]b_{n,j} = \frac{(2n-1+j)!}{(2n-1)!j!}[/tex]

Is there any algorithm that can be used to derive this result? I have a recurrence relation which is a bit more complex than this one.

[tex]b_{n,j+1} (j+1)(2n-1)(2n-2) = (2n-2+j)(2n-1+j)b_{n-1,j}[/tex]

which has the solution

[tex]b_{n,j} = \frac{(2n-1+j)!}{(2n-1)!j!}[/tex]

Is there any algorithm that can be used to derive this result? I have a recurrence relation which is a bit more complex than this one.