[math-fun] exact formulas for Motzkin numbers

Maybe Simon was looking at a very old copy of the OEIS. There are now several exact formulas for A001006. See the entry for more details. Here are two: %F A001006 a(n) = (-1/2) SUM (-3)^i C(1/2,i) C(1/2, j); i+j=n+2, i >= 0, j >= 0. %F A001006 a(n) = (1/(n+1)) * Sum_{i} (n+1)!/(i!*(i+1)!*(n-2*i)!) - Bernhart. NJAS