A119522 Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Formula

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.

Example

a(3) = -27 =
|.1..3..6|
|10.15.21|
|28.36.45|.
a(4) = 0 because of the singular matrix 0 =
|.1...3...6..10|
|15..21..28..36|
|45..55..66..78|
|91.105.120.136|.

Mathematica

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 *)

Crossrefs

Cf. A000217, A119493.

Sequence in context: A171740 A129663 A112646 * A070494 A334659 A350625

Adjacent sequences: A119519 A119520 A119521 * A119523 A119524 A119525

Keyword

easy,sign

Author

Jonathan Vos Post, May 27 2006

Extensions

More terms from Vaclav Kotesovec, Feb 24 2019

Status

approved