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%I #22 Mar 16 2020 02:52:48
%S 1,1,3,7,17,35,76,149,291,539,974,1691,2874,4730,7620,11986,18485,
%T 27944,41550,60744,87527,124338,174403,241650,331153,448987,602853,
%U 801943,1057615,1383343,1795578,2313595,2960656,3763879,4755505,5972927,7460196,9267980
%N Number of multigraphs with 5 nodes and n edges.
%D CRC Handbook of Combinatorial Designs, 1996, p. 650.
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 88, (4.1.18).
%D J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 517.
%H Andrew Howroyd, <a href="/A014395/b014395.txt">Table of n, a(n) for n = 0..1000</a>
%F 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)).
%t 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 *)
%o (PARI) concat([1], G(5, 40)) \\ See A191646 for G. - _Andrew Howroyd_, Mar 15 2020
%Y Row 5 of A192517.
%Y Cf. A001399, A003082, A014396, A014397, A014398.
%K easy,nonn
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Dec 23 1999