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 A059585 Number of labeled 3-node T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included). 2
 0, 0, 12, 68, 235, 636, 1478, 3088, 5958, 10800, 18612, 30756, 49049, 75868, 114270, 168128, 242284, 342720, 476748, 653220, 882759, 1178012, 1553926, 2028048, 2620850, 3356080, 4261140, 5367492, 6711093, 8332860, 10279166, 12602368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1). FORMULA a(n) = binomial(n + 7, n) - 3*binomial(n + 3, n) + 2*binomial(n + 1, n) = n*(n - 1)*(n + 1)*(n^4 + 28*n^3 + 323*n^2 + 1988*n + 4572)/5040. G.f.: x^2*(2-x)^2*(3-4*x+2*x^2)/(1-x)^8. [Colin Barker, Jun 25 2012] MAPLE for n from 0 to 100 do printf(`%d, `, n*(n - 1)*(n + 1)*(n^4 + 28*n^3 + 323*n^2 + 1988*n + 4572)/5040) od: CROSSREFS Cf. A059084, a(n)=A059584(n, 3), A059586. Sequence in context: A199415 A200204 A200205 * A213547 A050484 A096425 Adjacent sequences:  A059582 A059583 A059584 * A059586 A059587 A059588 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jan 23 2001 EXTENSIONS More terms from James A. Sellers, Jan 24 2001 STATUS approved

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