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%I #6 Feb 24 2019 04:36:03
%S 1,-8,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.
%F a(n) = determinant of n X n matrix of first n^2 nonzero terms of A000217(k) for k>0. a(n) = determinant of n X n matrix of k*(k+1)/2 for k from 1 through n^2.
%e a(3) = -27 =
%e |.1..3..6|
%e |10.15.21|
%e |28.36.45|.
%e a(4) = 0 because of the singular matrix 0 =
%e |.1...3...6..10|
%e |15..21..28..36|
%e |45..55..66..78|
%e |91.105.120.136|.
%t nmax = 100; Table[Det[Table[(k*(i-1) + j)*(k*(i-1) + j + 1)/2, {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* _Vaclav Kotesovec_, Feb 24 2019 *)
%Y Cf. A000217, A119493.
%K easy,sign
%O 1,2
%A _Jonathan Vos Post_, May 27 2006
%E More terms from _Vaclav Kotesovec_, Feb 24 2019