A379913 Let M_n be the n X n matrix M_(i,j)=1/(3^i+3^j), then a(n) is the denominator of det(M_n).

6, 432, 145800, 28934010000, 36195844320916875, 8087414520398390420149816875, 14739121497834560950873288612087606246265625, 24111787175394014554749263306909156210251310885835206605812890625, 30311902674167553291682092445492621447523310843996437232420613554400185533411542126171875

Offset: 1

Author

Robert Israel, Jan 06 2025

Keywords

• nonn

Examples

			For n = 3, the determinant of the matrix [1/6, 1/12, 1/30; 1/12, 1/18, 1/36; 1/30, 1/36, 1/54] is 1/145800, so a(3) = 145800.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..20

Crossrefs

Numerators are A069743.

Programs

Maple

g:= proc(n) local M;
  M:= Matrix(n,n,(i,j) -> 1/(3^i+3^j));
  denom(LinearAlgebra:-Determinant(M))
end proc:
map(g, [$1..10]);

PARI

a(n) = denominator(matdet(matrix(n, n, i, j, 1/(3^i+3^j)))); \\ Michel Marcus, Jan 06 2025