The Pascal-de Moivre Triangles*
نویسنده
چکیده
The coefficients of the Pascal triangle were generalized in 1756 by de Moivre [5]. Each row of a Pascal triangle contains a sequence of numbers that are the coefficients of the power series expansion for the binary expression (l + x)^. The de Moivre formula [2], [4], [5], [6] derives the coefficients of the power series for the generalized expansion of (1 + x + x + • • • + x^"^). Thus, for integers (J>2 andN> 1) and for 0<h<N(J-l), we define C(N,J;h) to be the coefficients of (x) in the expansion of (l + x + x + '-' + x-y = ZC(N,J;h)x. (1)
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