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Certain families of d-uniform hypergraphs are counted. In particular, the number of connected d-uniform hypergraphs with r vertices and r + k hyperedges, where k = o(log r/log tog r), is found. A hypergraph H is a pair (V,E) , where the set of hyperedges E is the family of subset of the vertex set V. A sequence of voelvl ...ekvk, where v; are vertices of H,doi:10.1016/s0012-365x(96)00076-3 fatcat:dydcuzj5dvgm3dr72exuq3uena