(OEIS A008292). Note that the rows sum to the successive factorials , , , , ....

The plot above shows the binary representations for the first 255 (top figure) and 511 (bottom figure) terms of a flattened Euler's number triangle.

Amazingly, the Z-transform of is the generator for the first rows of Euler's number triangle, when the th term of the transform is first cleared of its denominator
by multiplying through by . For example,