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A014395
Number of multigraphs with 5 nodes and n edges.
12
1, 1, 3, 7, 17, 35, 76, 149, 291, 539, 974, 1691, 2874, 4730, 7620, 11986, 18485, 27944, 41550, 60744, 87527, 124338, 174403, 241650, 331153, 448987, 602853, 801943, 1057615, 1383343, 1795578, 2313595, 2960656, 3763879, 4755505, 5972927, 7460196, 9267980
OFFSET
0,3
REFERENCES
CRC Handbook of Combinatorial Designs, 1996, p. 650.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 88, (4.1.18).
J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 517.
LINKS
FORMULA
G.f.: (x^21 + x^20 + 5*x^19 + 8*x^18 + 14*x^17 + 22*x^16 + 32*x^15 + 40*x^14 + 39*x^13 + 47*x^12 + 36*x^11 + 36*x^10 + 25*x^9 + 21*x^8 + 12*x^7 + 11*x^6 + 4*x^5 + 4*x^4 + x^3 + x^2 - x + 1)/((x^6 - 1)*(x^5 - 1)^2*(x^4 - 1)^2*(x^3 - 1)^2*(x - 1)^3*(x + 1)).
MATHEMATICA
CoefficientList[Series[PairGroupIndex[SymmetricGroup[5], s]/.Table[s[i]->1/(1-x^i), {i, 1, Binomial[5, 2]}], {x, 0, 30}], x] (* Geoffrey Critzer, Oct 14 2012 *)
PROG
(PARI) concat([1], G(5, 40)) \\ See A191646 for G. - Andrew Howroyd, Mar 15 2020
CROSSREFS
KEYWORD
easy,nonn
EXTENSIONS
More terms from Vladeta Jovovic, Dec 23 1999
STATUS
approved