delannoy_mem = dict()

def delannoy(n, m):
    if (n, m) not in delannoy_mem:
        if (n == 0) or (m == 0):
            resultat = 1
        else:
            resultat = delannoy(n - 1, m - 1) + delannoy(n - 1, m) + delannoy(n, m - 1)
        delannoy_mem[(n, m)] = resultat
    return delannoy_mem[(n, m)] 



# tests

assert delannoy(3, 3) == 63
assert delannoy(2, 1) == 5