A290539 Determinant of circulant matrix of order eight with entries in the first row that are (-1)^(j-1) * Sum_{k>=0} (-1)^k*binomial(n,8*k+j-1), for j=1..8.

1, 0, 0, 0, 0, 0, 0, 0, -8489565952, -31872959692800, -932158289501356032, -4169183582652459909120, -5144394740685202662359040, -2505627397073121215653085184, -500556279165026162974748835840, 0, 20396260728315877590754520243175424

Offset

0,9

Comments

a(n) = 0 for n == 7 (mod 8).

Links

Robert Israel, Table of n, a(n) for n = 0..428

Vladimir Shevelev, Combinatorial identities generated by difference analogs of hyperbolic and trigonometric functions of order n, arXiv:1706.01454 [math.CO], 2017.

Wikipedia, Circulant matrix

Maple

seq(LinearAlgebra:-Determinant(Matrix(8, 8, shape=Circulant[seq(
(-1)^(j-1)*add((-1)^k*binomial(n, 8*k+j-1), k=0..n/8), j=1..8)])), n=0..20); # Robert Israel, Aug 11 2017

Mathematica

ro[n_] := Table[(-1)^(j-1) Sum[(-1)^k*Binomial[n, 8k+j-1], {k, 0, n/8}], {j, 1, 8}];
M[n_] := Table[RotateRight[ro[n], m], {m, 0, 7}];
a[n_] := Det[M[n]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Aug 10 2018 *)

Crossrefs

Cf. A290285, A290286, A290535, A290540.

Sequence in context: A250865 A108880 A204500 * A017003 A017075 A017267

Adjacent sequences: A290536 A290537 A290538 * A290540 A290541 A290542

Keyword

sign

Author

Vladimir Shevelev and Peter J. C. Moses, Aug 05 2017

Status

approved