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COMMENTS
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The array A(n,k) = A(n-1,k+1) - A(n-1,k) of the sequence in the first row and higher-order sequences in followup rows starts:
2, 1, -1, -2, 1, 6, -3, ...
-1, -2, -1, 3, 5, -9, -31, ...
-1, 1, 4, 2, -14, -22, 82, ...
2, 3, -2, -16, -8, 104, 160, ...
1, -5, -14, 8, 112, 56, -1160, ...
-6, -9, 22, 104, -56, -1216, -608, ...
-3, 31, 82, -160, -1160, 608, 18880, ...
etc.
a(n) is an autosequence: Its inverse binomial transform is the sequence (up to a sign), which means top row and left column in the difference array have the same absolute values.
The main diagonal is the double of the first upper diagonal: A(n,n) = 2*A(n,n+1).
A(n,n+1) = (-1)^n*A005439(n), which also appears as the first upper diagonal of the difference array of A226158(n).
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