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Search: id:A131288
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| A131288 |
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Number of sets of subsets of an n-set such that the union is the whole set and the intersection is empty (not excluding the whole or the empty from being in the cover). |
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| 2, 1, 7, 193, 63775, 4294321153, 18446744022173838463, 340282366920938463205120190760593525761, 115792089237316195423570985008687907847825466794905548626109625623336235655679
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Number of covering sets of subsets of n-set is inverse binomial transform of number of sets of subsets. Number of coverings with empty intersection is (to within a unit parity flutter and a fudge unit when n = 0) inverse binomial transform of number of coverings, i.e. second inverse binomial transform of number of sets of subsets.
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FORMULA
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0^n - (-1)^n + double sum on k from 0 to n and t from 0 to k: (n choose k) (k choose t) (-1)^(n-t) 2^(2^t)
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CROSSREFS
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Cf. A003465 (coverings by non-empty subsets), A000371 = 2 x A003465 (coverings allowing empty block).
Sequence in context: A141516 A138346 A085073 this_sequence A111789 A021825 A152901
Adjacent sequences: A131285 A131286 A131287 this_sequence A131289 A131290 A131291
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KEYWORD
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nonn,nice
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AUTHOR
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David Pasino (davepasino(AT)yahoo.com), Sep 29 2007
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