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A119522 Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A070493

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

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Last modified July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)