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A059089 Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge excluded). 7

%I

%S 2,3,27,18209,2369751602470,5960531437867327674538684858601298,

%T 479047836152505670895481842190009123676957243077039687942939196956404642582185242435050

%N Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge excluded).

%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 Column sums of A059087.

%F a(n) = Sum_{k = 0..n} (-1)^(n-k)*A059086(k); a(n) = (1/n!)*Sum_{k = 0..n+1} stirling1(n+1, k)*floor(( 2^(k-1))!*exp(1)).

%e a(2)=27; There are 27 labeled T_0-hypergraphs with 2 distinct hyperedges (empty hyperedge excluded): 3 2-node hypergraphs, 12 3-node hypergraphs and 12 4-node hypergraphs.

%e a(3) = (1/3!)*(-6*[1!*e]+11*[2!*e]-6*[4!*e]+[8!*e]) = (1/3!)*(-6*2+11*5-6*65+109601) = 18209, 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+1,k)*floor((2^(k-1))!*exp(1)), k=0..n+1)) od:

%Y Cf. A059084-A059088.

%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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Last modified December 7 08:58 EST 2022. Contains 358653 sequences. (Running on oeis4.)