A096732 a(n)=det(M_n) where M_n is the n X n matrix m(i,j)=i^j*j^i.
1, 12, 4284, 84720384, 148993369113600, 34155172566092379340800, 1406681240638328150516203644518400, 13722109275339434419337247034130459935742361600
Offset: 1
Programs
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Mathematica
Table[Det[Table[i^j j^i,{i,n},{j,n}]],{n,8}] (* Harvey P. Dale, Jun 26 2021 *) -
PARI
for(n=1,10,print1(matdet(matrix(n,n,i,j,i^j*j^i)),","))
Formula
Conjecture: lim_{n->oo} a(n)^(1/n^2)/n = 2*exp(-3/2). - Vaclav Kotesovec, Apr 19 2024