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

%S 1,1,1,1,1,2,4,7,3,1,6,17,50,47,25,6,1,24,85,370,617,526,235,65,10,1,

%T 120,499,2929,7700,10205,7173,3026,800,140,15,1,720,3388,25165,95907,

%U 189224,197893,121521,47145,12236,2170,266,21,1,5040,26200

%N Consider the family of multigraphs enriched by the species of cycles. Sequence gives the triangle read by rows giving coefficients of polynomials arising from enumeration of those multigraphs on n edges.

%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^2, x^2+x^3+x^4, 2x^2+4x^3+7x^4+3x^5+x^6, 6x^2+17x^3+50x^4+47x^5+25x^6+6x^7+x^8, ...

%K nonn,tabf

%O 0,6

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