Let a=(a1,a2,…,an) and e=(e1,e2,…,en) be real sequences. Denote by Me→a the (n+1)×(n+1) matrix whose (m,k) entry (m,k∈{0,…,n}) is coefficient of polynomial (x−a1)⋯(x−ak) in expansion (x−e1)⋯(x−em) as a linear combination polynomials 1,x−a1,…,(x−a1)⋯(x−am). By appropriate choice e can encode many familiar doubly-indexed combinatorial sequences, such binomial coefficients, Stirling numbers both k...
