

A059085


Number of labeled nnode T_0hypergraphs without multiple hyperedges (empty hyperedge included).


8



2, 4, 12, 216, 64152, 4294320192, 18446744009290559040, 340282366920938463075992982635439125760, 115792089237316195423570985008687907843742078391854287068422946583140399879680
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OFFSET

0,1


COMMENTS

A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.


LINKS



FORMULA

a(n) = Sum_{k=0..n} stirling1(n, k)*2^(2^k).
E.g.f.: Sum(2^(2^n)*log(1+x)^n/n!, n=0..infinity) = Sum(log(2)^n*(1+x)^(2^n)/n!, n=0..infinity).  Vladeta Jovovic, May 10 2004


EXAMPLE

There are 216 labeled 3node T_0hypergraphs without multiple hyperedges (empty hyperedge included): 12 with 2 hyperedges, 44 with 3 hyperedges,67 with 4 hyperedges, 56 with 5 hyperedges, 28 with 6 hyperedges, 8 with 7 hyperedges and 1 with 8 hyperedges.


MAPLE

with(combinat): for n from 0 to 15 do printf(`%d, `, sum(stirling1(n, k)*2^(2^k), k=0..n)) od:


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



