A060536 Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 6 labeled nodes.

1, 15, 45, 90, 495, 1866, 5990, 19920, 62655, 186525, 526470, 1403265, 3530000, 8388495, 18884475, 40442635, 82775970, 162663240, 308201500, 565176105, 1006419120, 1745321275, 2955037455, 4895398755, 7950135835, 12677752431

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..25.

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

Formula

G.f.: - (6*x^25 - 30*x^24 + 60*x^23 + 615*x^22 - 9280*x^21 + 54909*x^20 - 186150*x^19 + 404285*x^18 - 581340*x^17 + 522915*x^16 - 172878*x^15 - 289605*x^14 + 590880*x^13 - 581955*x^12 + 337755*x^11 - 67650*x^10 - 74150*x^9 + 84315*x^8 - 42870*x^7 + 10410*x^6 + 888*x^5 - 1590*x^4 + 535*x^3 - 75*x^2 + 1)/(x - 1)^15. 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: A164788 A033849 A194715 * A014634 A303857 A278337

Adjacent sequences: A060533 A060534 A060535 * A060537 A060538 A060539

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 01 2001

Status

approved