8-ary mekso operator: the X1th nonnegative sum of X2 mutually-distinct perfect X3th-powers (i.e.: of integers) in X4 mutually truly-distinct ways, requiring exactly X5 terms to be negative in each sum (counting with(out^X6) multiplicity), requiring exactly X7 terms to be repeated between sums (counting with(out^X8) multiplicity), according to the usual ordering of the integers.
By default, X1 = 1, X5 = X6 = X7 = X8 = 0. Use "su'e" in X5 or X6 for weaker but bounded criteria (this will 'cancel' the corresponding "exactly"). For i being 6 or 8, if Xi is even, then "with multiplicity" is meant in the corresponding clause/requirement which is governed by this parameter; else, Xi is to be odd and "without multiplicity" is meant there. 0 is a valid summand and may be used multiple times. "Truly-distinct ways" in this context includes meanings such as "ignoring both parenthesis/priority and commutation/permutation of terms".