exact formulas for Motzkin numbers

N. J. A. Sloane njas at research.att.com
Tue Mar 23 23:09:54 CET 2004

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.


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