A060537 Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 7 labeled nodes.

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.

Links

Table of n, a(n) for n=0..22.

Vladeta Jovovic, Generating functions for homeomorphically irreducible multigraphs on n labeled nodes

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

Cf. A003514, A060516, A060533-A060537.

Sequence in context: A069499 A068142 A126229 * A116689 A235876 A279763

Adjacent sequences: A060534 A060535 A060536 * A060538 A060539 A060540

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 01 2001

Status

approved