依次写下(x+1)~0,(x+1)~1,(x+1)~2,(x+1)~3等的展开式,则各展开式的系数将构成一个三角形数阵,如图1所示.13世纪的中国数学家杨辉在其著作《详解九章算法》中提到过这个三角形数阵,因此这个三角形数阵也被人叫做“杨辉三角”.杨辉在书中指出,此表是由中国数学家贾宪在11世纪发现的.因此, (X + 1) ~ 1, (x + 1) ~ 1, (x + 1) ~ 2, (x + 1) ~ 3 and so on, the coefficients of each expansion will form a triangular number Array, shown in Figure 1. 13th century Chinese mathematician Yang Hui in his book “Detailed Nine chapters algorithm” mentioned in the triangular array, so the triangular array is also called "Yang Hui Triangle The book states that this table was discovered by Chinese mathematician Jia Xian in the 11th century and therefore,