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a(n) is the permanent of the n X n matrix M(n) whose generic M[i, j] = j*(10^i - 1)/9 with 1 <= i, j <= n.
1

%I #13 Sep 17 2023 10:01:45

%S 1,1,44,43956,781361856,217042789550400,868170290030441798400,

%T 47267044397174696636039097600,33612120124091913005718848881499750400,

%U 302509080814318135934642422882028113666502246400,33612120087118580872578956587618207930922159448149975040000

%N a(n) is the permanent of the n X n matrix M(n) whose generic M[i, j] = j*(10^i - 1)/9 with 1 <= i, j <= n.

%C For n > 1, the matrix M(n) is singular.

%e a(3) = 43956:

%e [ 1, 2, 3]

%e [ 11, 22, 33]

%e [111, 222, 333]

%t M[i_,j_]:=j(10^i-1)/9; Join[{1},Table[Permanent[Table[M[i,j],{i,n},{j,n}]],{n,10}]]

%o (PARI) a(n) = matpermanent(matrix(n,n,i,j,j*(10^i - 1)/9)); \\ _Michel Marcus_, Sep 17 2023

%Y Cf. A365644.

%K nonn

%O 0,3

%A _Stefano Spezia_, Sep 14 2023