A349099 a(n) is the permanent of the n X n matrix M(n) defined as M(n)[i,j] = i*j (mod n + 1).

1, 1, 5, 32, 1074, 12600, 1525292, 34078720, 4072850100, 263459065600, 106809546673488, 2254519427530752, 3172225081523720416, 210351382651302645760, 45654014718074873700000, 11122845097194072534155264, 18156837198112938091803999360, 795289872611524024920215715840

Offset: 0

Author

Stefano Spezia, Mar 25 2022

Keywords

• nonn

Comments

Det(M(n)) = 0 iff n = 4 or n > 5.

Rank(M(n)) = A088922(n+1).

Tr(M(n)) = A048153(n+1).

Examples

			See A352620 for the examples of matrix M(n).
		

Crossrefs

Cf. A352620.

Cf. A048153, A074930, A088922, A160255.

Programs

Maple

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
         Matrix(n, (i, j)-> (i*j) mod (n+1)))):
seq(a(n), n=0..16);  # Alois P. Heinz, Mar 25 2022

Mathematica

Join[{1},Table[Permanent[Table[Mod[j*Table[i, {i, n}], n+1], {j, n}]], {n, 17}]]

PARI

a(n) = matpermanent(matrix(n,n,i,j,(i*j)%(n+1))); \\ Michel Marcus, Mar 26 2022