Feb 8, 2022
Multinomial coefficients and Pascal's Simplex
For binomials [ (a+b)ⁿ ] the use of Pascal's triangle is helpful. In Pascal's triangle each single row in the triangle defines the coefficients of binomials of each n-value.
For trinomials [ (a+b+c)ⁿ ] this pattern can be extended to a 3-dimensional Pascal's tetrehedron, where each level (and hence a complete triangle) in that tetrehedron defines the coefficients of trinomials of each value of n.
As for quadrinomials [ (a+b+c+d)ⁿ ] the coefficients require an own tetrahedron for each value of n.
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