The fractions are an autosequence of the second kind. See the link.
Array of fractions and successive differences:
1, 1/2, 2/3, 3/4, 1, ...
-1/2, 1/6, 1/12, 1/4, 1/3, ...
2 /3, -1/12, 1/6, 1/12, 4/21, ...
-3/4, 1/4, -1/12, 3/28, 3/56, ...
1, -1/3, 4/21, -3/56, 11/126, ...
...
The sequence of fractions being an autosequence, it can be noticed that first column, which is the inverse binomial transform of first row, is identical to the sequence, up to alternating signs.
In addition, main diagonal is twice the first upper diagonal (autosequence of the second kind).
