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%I #13 Feb 10 2022 10:04:26
%S 1,1,7,169,10388,1324344,305668180,116145817656,67770421715800,
%T 57594670663866124,68393751368082128320,109765035421144948709232,
%U 231657098706747226470685920,628412716450312334529486247152,2149132484027947970192241804640128,9113755489596517688997731211571700256
%N a(n) is the permanent of the n X n matrix M(n) that is defined as M[i,j,n] = A351153(n, min(i, j)) + abs(i - j).
%C Conjectures: (Start)
%C det(M(0)) = det(M(1)) = 1 and det(M(n)) = -(n - 2)! for n > 1.
%C abs(det(M(n))) = abs(A159333(n-2)). (End)
%e a(3) = 169:
%e 1 2 3
%e 2 4 5
%e 3 5 6
%e a(4) = 10388:
%e 1 2 3 4
%e 2 5 6 7
%e 3 6 8 9
%e 4 7 9 10
%t A351153[n_,k_]:=n(k-1)-k(k-3)/2; M[i_,j_,n_]:=A351153[n,Min[i,j]]+Abs[i-j]; a[n_]:=Permanent[Table[M[i,j,n],{i,n},{j,n}]]; Join[{1},Array[a,15]]
%o (PARI) t(n, k) = n*(k-1) - k*(k-3)/2; \\ A351153
%o a(n) = matpermanent(matrix(n, n, i, j, t(n, min(i, j)) + abs(i - j))); \\ _Michel Marcus_, Feb 03 2022
%Y Cf. A000142, A003983, A049581, A159333, A351153.
%K nonn
%O 0,3
%A _Stefano Spezia_, Feb 02 2022
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