Is there a formular to the determinant of Hessenberg?

07 July 2018 0 1K Report

For the determinant of an 5n×5n Hessenberg matrix

[[1,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,0],[0,1,2,1,0,0,0,0,0],[0,0,1,2,1,0,0,0,0],[0,0,0,1,2,1,0,0,0],[0,0,0,0,1,3,3,1,0],[0,0,0,0,0,1,3,3,1],[0,0,0,0,0,0,1,4,6],[0,0,0,0,0,0,0,1,4]], is there a formular involve a binomial?

I already have a formular about

|[[1,0,0,0,0],[1,8,28,56,70],[0,1,15,105,455],[0,0,1,22,231],[0,0,0,1,29]]|=binomial((7+1)*5, 5)/(7*5+1).

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