A059086 - OEIS

%I #7 May 10 2013 12:44:33

%S 2,5,30,18236,2369751620679,5960531437867327674541054610203768,

%T 479047836152505670895481842190009123676957243077039693903470634823732317120870101036348

%N Number of labeled T_0-hypergraphs with n distinct 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.

%F a(n) = (1/n!)*Sum_{k = 0..n} stirling1(n, k)*floor((2^k)!*exp(1)).

%e a(2)=30; There are 30 labeled T_0-hypergraphs with 2 distinct hyperedges (empty hyperedge included): 1 1-node hypergraph, 5 2-node hypergraphs, 12 3-node hypergraphs and 12 4-node hypergraphs.

%e a(3) = (1/3!)*(2*[2!*e]-3*[4!*e]+[8!*e]) = (1/3!)*(2*5-3*65+109601) = 18236, where [k!*e] := floor (k!*exp(1)).

%p with(combinat): Digits := 1000: for n from 0 to 8 do printf(`%d,`,(1/n!)*sum(stirling1(n, k)*floor((2^k)!*exp(1)), k=0..n)) od:

%Y Column sums of A059084.

%Y Cf. A059084, A059085, 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