Factorials third kind

A more fruitful avenue of research may be the search for factorions of the second kind, which are formed by the product of the factorial values for each of their digits. Additionally, hypothetical factorions of the third kind are formed by grouping digits. For example, a factorion of the third kind might have the form... 

The table of results is laid out in a column, and a second column is constructed in which in the first four rows the results would be added sequentially in pairs, e. g. xi + x2, x3 + jc4, 5 + X(, etc., and the lower four rows are calculated by subtracting the second value from the preceding value thus, x2 — x, jc4 — x3 etc., a third column is prepared from these results by carrying out the same sequence of operations. The process is continued until there are as many columns as the number of variables. Thus in the present three-variable, two level-study the process is repeated three times (Table 15.1), and in the general n-variable, two-level case it is repeated n times. (The general description of trials of this kind where there are n variables and two levels, is 2" factorial trials ). 

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