A071410 Determinant of the 2n X 2n matrix m(i,j) = i^j - j^i.

1, 1, 196, 65028096, 1540115470208876544, 861787404007697994335390269440000, 3024149801599872168810739614376506649075557335040000, 25610879735369429335666530857036523659955793212506655095941286757767577600000000

Offset: 0

Author

Benoit Cloitre, May 28 2002

Keywords

• easy
• nonn

Comments

Determinant of the (2n+1) X (2n+1) matrix m(i,j) = i^j-j^i is zero.

Programs

Mathematica

Join[{1}, Table[Det[Table[i^j - j^i, {i, 1, 2*n}, {j, 1, 2*n}]], {n, 1, 8}]] (* Vaclav Kotesovec, Apr 18 2024 *)

PARI

for(n=1,20,print1(matdet(matrix(2*n,2*n,i,j,i^j-j^i)),","))

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 25 2023