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A060577
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Number of homeomorphically irreducible general graphs on 2 labeled nodes and with n edges.
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1
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1, 1, 4, 6, 11, 17, 24, 32, 41, 51, 62, 74, 87, 101, 116, 132, 149, 167, 186, 206, 227, 249, 272, 296, 321, 347, 374, 402, 431, 461, 492, 524, 557, 591, 626, 662, 699, 737, 776, 816, 857, 899, 942, 986, 1031, 1077, 1124, 1172, 1221, 1271, 1322, 1374, 1427
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OFFSET
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0,3
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COMMENTS
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A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
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LINKS
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Table of n, a(n) for n=0..52.
V. Jovovic, Generating functions for homeomorphically irreducible general graphs on n labeled nodes
V. Jovovic, Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges
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FORMULA
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G.f.: (2*x^5 - 4*x^4 + 4*x^3 - 4*x^2 + 2*x - 1)/(x - 1)^3. E.g.f. for homeomorphically irreducible general graphs with n nodes and k edges is (1 + x*y)^( - 1/2)*exp( - x*y/2 + x^2*y^2/4)*Sum_{k >= 0} 1/(1 - x)^binomial(k + 1, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.
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MAPLE
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gf := (2*x^5 - 4*x^4 + 4*x^3 - 4*x^2 + 2*x - 1)/(x - 1)^3: s := series(gf, x, 100): for i from 0 to 100 do printf(`%d, `, coeff(s, x, i)) od:
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CROSSREFS
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Cf. A003514, A060516, A060533-A060537, A060576-A060581.
Sequence in context: A190499 A190564 A008369 * A197985 A058579 A022318
Adjacent sequences: A060574 A060575 A060576 * A060578 A060579 A060580
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Apr 04 2001
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EXTENSIONS
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More terms from James A. Sellers, Apr 04 2001
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STATUS
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approved
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