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A059085 Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included). 8

%I #11 Jul 08 2015 23:51:22

%S 2,4,12,216,64152,4294320192,18446744009290559040,

%T 340282366920938463075992982635439125760,

%U 115792089237316195423570985008687907843742078391854287068422946583140399879680

%N Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included).

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

%H V. Jovovic, <a href="/A059084/a059084.pdf">Illustration of initial terms of A059084, A059085</a>

%F Row sums of A059084.

%F a(n) = Sum_{k=0..n} stirling1(n, k)*2^(2^k).

%F 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

%e There are 216 labeled 3-node T_0-hypergraphs 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.

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

%Y Cf. A059084, A059086, A059087-A059089.

%K easy,nonn

%O 0,1

%A Goran Kilibarda, _Vladeta Jovovic_, Dec 27 2000

%E More terms from _James A. Sellers_, Jan 24 2001

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