|
| |
|
|
A131288
|
|
a(n) = number of ways to choose a collection C of subsets of U = [1,2,...,n] such that Union_{S in C} = U, Intersection_{S in C} = empty set.
|
|
1
| |
|
|
2, 1, 7, 193, 63775, 4294321153, 18446744022173838463, 340282366920938463205120190760593525761, 115792089237316195423570985008687907847825466794905548626109625623336235655679
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| The collection C may include the empty set and/or U.
The number of covers of an n-set (A000371) is the inverse binomial transform of number of sets of subsets. The number of coverings with empty intersection is (to within a unit parity flutter and a fudge unit when n = 0) the inverse binomial transform of the number of coverings, i.e. the second inverse binomial transform of number of sets of subsets.
|
|
|
FORMULA
| a(n) = 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)
|
|
|
MATHEMATICA
| a[n_] = (-1)^(n+1) + Sum[Binomial[n, k]*Binomial[k, t]*(-1)^(n-t)*2^(2^t), {k, 0, n}, {t, 0, k}]; a[0] = 2;
a /@ Range[0, 8] (* From Jean-François Alcover, Jul 20 2011, after formula *)
|
|
|
CROSSREFS
| Cf. A003465 (coverings by nonempty subsets), A000371 = 2 x A003465 (coverings allowing the empty set as one of the subsets).
Sequence in context: A183272 A138346 A085073 * A111789 A179447 A021825
Adjacent sequences: A131285 A131286 A131287 * A131289 A131290 A131291
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| David Pasino (davepasino(AT)yahoo.com), Sep 29 2007
|
| |
|
|
