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A060535
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Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 5 labeled nodes.
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1
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1, 10, 15, 30, 165, 430, 1170, 3180, 7935, 18610, 40948, 84570, 164740, 304690, 538630, 915574, 1504135, 2398460, 3725495, 5653790, 8404075, 12261860, 17592335, 24857870, 34638440, 47655326, 64798470, 87157890, 116059590
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OFFSET
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0,2
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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..28.
Vladeta Jovovic, Generating functions for homeomorphically irreducible multigraphs on n labeled nodes
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FORMULA
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G.f.: (5*x^18 - 20*x^17 + 30*x^16 + 58*x^15 - 745*x^14 + 2790*x^13 - 5270*x^12 + 5010*x^11 - 711*x^10 - 4380*x^9 + 6270*x^8 - 4470*x^7 + 1535*x^6 + 178*x^5 - 450*x^4 + 210*x^3 - 40*x^2 + 1)/(x - 1)^10. E.g.f. for homeomorphically irreducible multigraphs 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, 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.
Sequence in context: A051990 A182427 A171956 * A037379 A055049 A128703
Adjacent sequences: A060532 A060533 A060534 * A060536 A060537 A060538
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Apr 01 2001
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STATUS
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approved
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