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Search: id:A060580
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| A060580 |
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Number of homeomorphically irreducible general graphs on 5 labeled nodes and with n edges. |
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+0
1
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| 1, 10, 40, 185, 765, 2845, 10220, 33885, 105185, 305465, 830811, 2119875, 5091525, 11565505, 24977315, 51552005, 102175360, 195301015, 361365695, 649360880, 1136438375, 1941722170, 3245874555, 5318438260, 8555568895, 13531506921
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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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.: - (5*x^22 - 20*x^21 + 23*x^20 - 815*x^19 + 8110*x^18 - 37255*x^17 + 104890*x^16 - 204469*x^15 + 296720*x^14 - 337455*x^13 + 310150*x^12 - 229885*x^11 + 131054*x^10 - 50485*x^9 + 6490*x^8 + 7255*x^7 - 6730*x^6 + 3242*x^5 - 995*x^4 + 180*x^3 - 5*x^2 - 5*x + 1)/(x - 1)^15. 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: A075060 A002066 A061991 this_sequence A118266 A054885 A000449
Adjacent sequences: A060577 A060578 A060579 this_sequence A060581 A060582 A060583
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 03 2001
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