The nth central trinomial coefficient is defined as the coefficient of x^n in the expansion of (1 + x + x^2)^n. It is therefore the middle column of the trinomial triangle, i.e., the trinomial coefficient (n 0)_2. The first few central trinomial coefficients for n = 1, 2, ... are 1, 3, 7, 19, 51, 141, 393, ... (OEIS A002426). The central trinomial coefficient is also gives the number of permutations of n symbols, each -1, 0, or 1, which sum to 0. For example, there are seven such permutations of three symbols: {-1, 0, 1}, {-1, 1, 0}, {0, -1, 1}, {0, 0, 0}, and {0, 1, -1}, {1, -1, 0}, {1, 0, -1}.

central binomial coefficient | central fibonomial coefficient | trinomial coefficient