

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
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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*(i1) + j)*(k*(i1) + 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



