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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).

%I A349099 #19 Mar 27 2022 16:46:14
%S A349099 1,1,5,32,1074,12600,1525292,34078720,4072850100,263459065600,
%T A349099 106809546673488,2254519427530752,3172225081523720416,
%U A349099 210351382651302645760,45654014718074873700000,11122845097194072534155264,18156837198112938091803999360,795289872611524024920215715840
%N 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).
%C A349099 Det(M(n)) = 0 iff n = 4 or n > 5.
%C A349099 Rank(M(n)) = A088922(n+1).
%C A349099 Tr(M(n)) = A048153(n+1).
%e A349099 See A352620 for the examples of matrix M(n).
%p A349099 a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
%p A349099          Matrix(n, (i, j)-> (i*j) mod (n+1)))):
%p A349099 seq(a(n), n=0..16);  # _Alois P. Heinz_, Mar 25 2022
%t A349099 Join[{1},Table[Permanent[Table[Mod[j*Table[i, {i, n}], n+1], {j, n}]], {n, 17}]]
%o A349099 (PARI) a(n) = matpermanent(matrix(n,n,i,j,(i*j)%(n+1))); \\ _Michel Marcus_, Mar 26 2022
%Y A349099 Cf. A352620.
%Y A349099 Cf. A048153, A074930, A088922, A160255.
%K A349099 nonn
%O A349099 0,3
%A A349099 _Stefano Spezia_, Mar 25 2022