A069740 Let M_n be the n X n matrix M_(i,j)=1/(i+j+ij); a(n) is the numerator of det(M_n).

1, 1, 1, 1, 1, 4, 1, 64, 4, 65536, 512, 33554432, 65536, 68719476736, 6442450944, 9007199254740992, 281474976710656, 220326730624766167090200576, 340010386766614455386112, 486777830487640090174734030864384, 2619273682248342113770827134478065860608

Offset

0,6

Comments

Is a(n) always of the form 2^u*3^v?

The answer to above question is: no, a(39) = 5*2^570*3^126. - Alois P. Heinz, Feb 21 2025

Links

Table of n, a(n) for n=0..20.

Maple

a:= n-> numer(LinearAlgebra[Determinant](Matrix(n, (i, j)-> 1/(i+j+i*j)))):
seq(a(n), n=0..20);  # Alois P. Heinz, Feb 21 2025

Mathematica

a[n_]:=Numerator[Det[Table[1/(i+j+i*j), {i, n}, {j, n}]]]; Join[{1}, Array[a, 20]] (* Stefano Spezia, Feb 21 2025 *)

Prog

(PARI) a(n) = numerator(matdet(matrix(n, n, i, j, 1/(i*j+i+j))));

Crossrefs

Sequence in context: A278578 A368266 A338681 * A173008 A381272 A298828

Adjacent sequences: A069737 A069738 A069739 * A069741 A069742 A069743

Keyword

easy,frac,nonn,changed

Author

Benoit Cloitre, Apr 21 2002

Extensions

a(0) = 1 prepended by and a(20) from Stefano Spezia, Feb 21 2025

Status

approved