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I'm trying to solve this recurrence with two variables.

RSolve[g[d, n] == 1 + g[d - 1, n] + g[d - 1, n - 1] && 
  g[d, 0] == g[0, n] == 0, g[d, n], {d, n}]

My boundary conditions are that g[d, 0] == g[0, n] == 0 for all d,n . But when I plug this in, I get the same input back with no error message.

Am I inputting the recurrence incorrectly? Or is Mathematica simply unable to find a closed form?

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I believe that you are using the correct syntax. –  Szabolcs Feb 3 '13 at 21:45
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It is a known sequence oeis.org/… –  belisarius Feb 4 '13 at 2:30

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