login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060536 Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 6 labeled nodes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)