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A060581
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Number of homeomorphically irreducible general graphs on 6 labeled node and with n edges.
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6
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1, 15, 81, 441, 2151, 9957, 43122, 174162, 666267, 2403987, 8183601, 26281065, 79660856, 228180456, 618992466, 1595081266, 3918506466, 9211519476, 20797923546, 45258309066, 95225448306, 194283668576, 385361919996
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OFFSET
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0,2
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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..22.
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.: (6*x^30 - 30*x^29 - 90*x^28 + 898*x^27 - 5703*x^26 + 67854*x^25 - 552925*x^24 + 2795730*x^23 - 9663357*x^22 + 24476292*x^21 - 47540991*x^20 + 73129860*x^19 - 91373250*x^18 + 94675608*x^17 - 82549758*x^16 + 60794764*x^15 - 37293240*x^14 + 18277860*x^13 - 6426742*x^12 + 945252*x^11 + 680499*x^10 - 726250*x^9 + 423825*x^8 - 187536*x^7 + 66981*x^6 - 19092*x^5 + 4065*x^4 - 560*x^3 + 24*x^2 + 6*x - 1)/(x - 1)^21. 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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CROSSREFS
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Cf. A003514, A060516, A060533-A060537, A060576-A060581.
Sequence in context: A055815 A102360 A213552 * A065103 A108674 A050405
Adjacent sequences: A060578 A060579 A060580 * A060582 A060583 A060584
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Vladeta Jovovic, Apr 03 2001
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STATUS
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approved
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