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A060535 Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 5 labeled nodes. 1
1, 10, 15, 30, 165, 430, 1170, 3180, 7935, 18610, 40948, 84570, 164740, 304690, 538630, 915574, 1504135, 2398460, 3725495, 5653790, 8404075, 12261860, 17592335, 24857870, 34638440, 47655326, 64798470, 87157890, 116059590 (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..28.

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

FORMULA

G.f.: (5*x^18 - 20*x^17 + 30*x^16 + 58*x^15 - 745*x^14 + 2790*x^13 - 5270*x^12 + 5010*x^11 - 711*x^10 - 4380*x^9 + 6270*x^8 - 4470*x^7 + 1535*x^6 + 178*x^5 - 450*x^4 + 210*x^3 - 40*x^2 + 1)/(x - 1)^10. 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: A182427 A171956 A271743 * A239595 A037379 A055049

Adjacent sequences:  A060532 A060533 A060534 * A060536 A060537 A060538

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Apr 01 2001

STATUS

approved

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Last modified February 24 17:29 EST 2020. Contains 332209 sequences. (Running on oeis4.)