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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

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)