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A060537
Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 7 labeled nodes.
11
1, 21, 105, 266, 1386, 6678, 25403, 100506, 384678, 1393903, 4831890, 15955485, 50080478, 149211930, 421819950, 1132236630, 2890927935, 7040892159, 16411041500, 36733789575, 79230165105, 165194651065, 333926559540
OFFSET
0,2
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
FORMULA
G.f.: (7*x^33 - 42*x^32 + 105*x^31 + 3598*x^30 - 64995*x^29 + 498369*x^28 - 2213029*x^27 + 6169800*x^26 - 10213560*x^25 + 4476990*x^24 + 27664014*x^23 - 97812519*x^22 + 197723150*x^21 - 296237340*x^20 + 352014180*x^19 - 334492361*x^18 + 243984426*x^17 - 117769575*x^16 + 9628325*x^15 + 45726945*x^14 - 50729175*x^13 + 31353175*x^12 - 11717370*x^11 + 1358280*x^10 + 1395765*x^9 - 1068648*x^8 + 395328*x^7 - 77805*x^6 + 882*x^5 + 4095*x^4 - 1141*x^3 + 126*x^2 - 1)/(x - 1)^21. 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!.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 01 2001
STATUS
approved