41CL Quiz: Determinant of 30x30 anti-Identity matrix

[Gerson W. Barbosa]

(06-02-2018 11:41 PM)Valentin Albillo Wrote:  Consider the determinant D(N) = determinant of this NxN matrix:
 
      3    1    1 ... 1
      1    4    1 ... 1
      1    1    5 ... 1
      ... ... ... ... ...
      1    1    1 ... N+2

For example, D(3) = 50. Now compute and time D(11), D(13),D(30).

If you succeed in getting the correct integer values, see if you can find an exact formula for D(N)    (Hint: after a while, D(n) ends with more and more 0's).

On my HP 50g:

D11 = 1486442880.
D13 = 283465647360.
D30 = 3.31153874629E34

« → n
« '(n+1)!*(Psi(n+2)-Psi(1))' EVAL
»
»

Probably not the formula you have in mind, but that’s what I could get so far.

D(n) = (n + 1)!*Hn+1

Regards,

Gerson.