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Consider the family of multigraphs enriched by the species of linear order. Sequence gives the triangle read by rows giving coefficients of polynomials arising from enumeration of those multigraphs on n edges, arcs and loops.
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%I #10 Jun 25 2017 14:55:52

%S 1,1,2,2,14,13,4,6,102,268,219,66,8,24,828,4668,7909,5309,1659,248,16,

%T 120,7500,80100,248870,303932,175783,53465,8950,800,32,720,75240,

%U 1411680,7476690,15207810,14504410,7361796,2150541,376375,39540

%N Consider the family of multigraphs enriched by the species of linear order. Sequence gives the triangle read by rows giving coefficients of polynomials arising from enumeration of those multigraphs on n edges, arcs and loops.

%D G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

%H G. Paquin, <a href="/A038205/a038205.pdf">Dénombrement de multigraphes enrichis</a>, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

%e 1, x+2x^2, 2x+14x^2+13x^3+4x^4, 6x+102x^2+268x^3+219x^4+66x^5+8x^6, 24x+828x^2+4668x^3+7909x^4+5309x^5+1659x^6+248x^7+16x^8, ...

%K nonn,tabf

%O 0,3

%A _N. J. A. Sloane_, Oct 26 2004