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 A060581 Number of homeomorphically irreducible general graphs on 6 labeled node and with n edges. 6
 1, 15, 81, 441, 2151, 9957, 43122, 174162, 666267, 2403987, 8183601, 26281065, 79660856, 228180456, 618992466, 1595081266, 3918506466, 9211519476, 20797923546, 45258309066, 95225448306, 194283668576, 385361919996 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2. REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983. LINKS FORMULA 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!. CROSSREFS Cf. A003514, A060516, A060533-A060537, A060576-A060581. Sequence in context: A309336 A266288 A213552 * A253222 A284900 A065103 Adjacent sequences:  A060578 A060579 A060580 * A060582 A060583 A060584 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Apr 03 2001 STATUS approved

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)