A119537 Determinant of n X n matrices of first n^2 denumerants (A000115).

1, 0, -3, -3, 0, -54, 343, 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

1,3

Comments

Conjecture: a(n>7)=0. - Robert G. Wilson v, Jun 07 2006

Links

Table of n, a(n) for n=1..104.

Formula

a(n) = determinant[A000115(k) from k=1 to n^2)].

Example

a(6) = -54 = -2 * 3^3. a(7) = 343 = 7^3.
a(8) = 0 because of the singular matrix 0 =
|..1...1...2...2...3...4...5...6|
|..7...8..10..11..13..14..16..18|
|.20..22..24..26..29..31..34..36|
|.39..42..45..48..51..54..58..61|
|.65..68..72..76..80..84..88..92|
|.97.101.106.110.115.120.125.130|
|135.140.146.151.157.162.168.174|
|180.186.192.198.205.211.218.224|.

Mathematica

clst = CoefficientList[ Series[1/((1 - x)(1 - x^2)(1 - x^5)), {x, 0, 105^2 - 1}], x]; f[n_] := Det[ Partition[ Take[clst, n^2], n]]; Array[f, 100] (* Robert G. Wilson v *)

Crossrefs

Cf. A000115, A119493.

Sequence in context: A166553 A285863 A111843 * A338148 A338144 A031438

Adjacent sequences: A119534 A119535 A119536 * A119538 A119539 A119540

Keyword

easy,sign

Author

Jonathan Vos Post, May 28 2006

Extensions

More terms from Robert G. Wilson v, Jun 07 2006

Status

approved