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%I #9 Dec 10 2023 09:19:35
%S 1,2,-17,-2016,6941952,1183818240000,-15226366699929600000,
%T -20905103969704791244800000000,
%U 4118415008134762062658292598964224000000,150638206504104123857462570135784635511078912000000000
%N Determinant of the n X n matrix with entries (X+Y)^n.
%H Robert Israel, <a href="/A092415/b092415.txt">Table of n, a(n) for n = 0..30</a>
%e For n = 3:
%e [2^3, 3^3, 4^3]
%e [3^3, 4^3, 5^3]
%e [4^3, 5^3, 6^3]
%e =
%e [8,27,64]
%e [27,64,125]
%e [64,125,216]
%e with determinant: -2016.
%p f:= n -> LinearAlgebra:-Determinant(Matrix(n,n,(i,j) -> (i+j)^n)):
%p map(f, [$0..12]); # _Robert Israel_, Dec 10 2023
%o (PARI) for(j=0,15,m=matrix(j,j,X,Y,(X+Y)^j); print1(matdet(m), ", "))
%K sign
%O 0,2
%A _Jon Perry_, Mar 22 2004
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