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COMMENTS
| The general formula where each entry is chosen from the subsets of {1,..,k} is (2^n-1)^k. This may be shown by exhibiting a bijection to a set whose cardinality is obviously (2^n-1)^k, namely the set of all k-tuples with each entry chosen from the 2^n-1 proper subsets of {1,..,n}, i.e. for of the k entries {1,..,n} is forbidden. The bijection is given by (X_1,..,X_n) |-> (Y_1,..,Y_k) where for each j in {1,..,k} and each i in {1,..,n}, i is in Y_j if and only if j is in X_i. Sequence A060867 is the case where the entries are chosen from subsets of {1,2}.
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EXAMPLE
| a(1)=(2^1-1)^3=1 because only one tuple of length one, namely ({}) has an
empty intersection of its sole entry. a(2)=27 because the valid 2-tuples are: ({},{}),
({},{1}), ({},{2}), ({},{3}), ({},{1,2}), ({},{1,3}), ({},{2,3}), ({},{1,2,3}),
({1},{}), ({2},{}), ({3},{}), ({1,2},{}), ({1,3},{}), ({2,3},{}), ({1,2,3},{}),
({1},{2}), ({1},{3}), ({1},{2,3}), ({2},{1}), ({2},{3}), ({2},{1,3}), ({3},{1}),
({3},{2}), ({3},{1,2}), ({1,2},{3}), ({1,3},{2}), ({2,3},{1})
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