  A class P_{n,m,p}(x) of polynomials is defined. The combinatorial meaning of
its coefficients is given. Chebyshev polynomials are the special cases of
P_{n,m,p}(x). It is first shown that P_{n,m,p}(x) may be expressed in terms of
P_{n,0,p}(x). From this we derive that P_{n,2,2}(x) may be obtain in terms of
trigonometric functions, from which we obtain some of its important properties.
Some questions about orthogonality are also concerned. Furthermore, it is shown
that P_{n,2,2}(x) fulfills the same three terms recurrence as Chebyshev
polynomials. Some others recurrences for P_{n,m,p}(x) and its coefficients are
also obtained. At the end a formula for coefficients of Chebyshev polynomials
of the second kind is derived.
