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 A060514 Triangle T(n,k) of series-reduced (or homeomorphically irreducible) labeled graphs with n nodes and k edges, k=0..binomial(n,2). 4
 1, 1, 1, 1, 1, 3, 0, 0, 1, 6, 3, 4, 0, 0, 1, 1, 10, 15, 20, 5, 0, 5, 20, 15, 10, 1, 1, 15, 45, 75, 90, 96, 135, 315, 510, 760, 843, 765, 395, 105, 15, 1, 1, 21, 105, 245, 525, 777, 1302, 3045, 7455, 16275, 30135, 50190, 70805, 81690, 70605, 43239, 18774, 5880, 1330 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983. LINKS D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286. FORMULA E.g.f. : (1+x*y)^(-1/2)*exp(x*y/2-x^2*y^2/4)*Sum_{k=0..inf}((1+x)*exp(-x^2*y/(1+x*y)))^binomial(k, 2)*(exp(1/2*x^3*y^2/(1+x*y)))^k*x^k/k! EXAMPLE Triangle begins: [1], [1], [1, 1], [1, 3, 0, 0], [1, 6, 3, 4, 0, 0, 1], [1, 10, 15, 20, 5, 0, 5, 20, 15, 10, 1], [1, 15, 45, 75, 90, 96, 135, 315, 510, 760, 843, 765, 395, 105, 15, 1], [1, 21, 105, 245, 525, 777, 1302, 3045, 7455, 16275, 30135, 50190, 70805, 81690, 70605, 43239, 18774, 5880, 1330, 210, 21, 1], ... CROSSREFS Row sums: A003514. For connected graphs see A331437, A331438. Sequence in context: A202023 A080159 A144299 * A176788 A238129 A212221 Adjacent sequences:  A060511 A060512 A060513 * A060515 A060516 A060517 KEYWORD nonn,tabf AUTHOR Vladeta Jovovic, Mar 23 2001 STATUS approved

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Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)