A349099 - OEIS

%I #19 Mar 27 2022 16:46:14

%S 1,1,5,32,1074,12600,1525292,34078720,4072850100,263459065600,

%T 106809546673488,2254519427530752,3172225081523720416,

%U 210351382651302645760,45654014718074873700000,11122845097194072534155264,18156837198112938091803999360,795289872611524024920215715840

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

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

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

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

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

%p a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](

%p          Matrix(n, (i, j)-> (i*j) mod (n+1)))):

%p seq(a(n), n=0..16);  # _Alois P. Heinz_, Mar 25 2022

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

%o (PARI) a(n) = matpermanent(matrix(n,n,i,j,(i*j)%(n+1))); \\ _Michel Marcus_, Mar 26 2022

%Y Cf. A352620.

%Y Cf. A048153, A074930, A088922, A160255.

%K nonn

%O 0,3

%A _Stefano Spezia_, Mar 25 2022