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 A181320 Triangle T(n,m) read by rows: the number of series-parallel networks with n+2 vertices and m+n+1 edges. 0
 1, 1, 1, 2, 7, 5, 6, 48, 91, 49, 24, 360, 1304, 1697, 729, 120, 3000, 17910, 41440, 41051, 14641, 720, 27720, 249900, 899730, 1524282, 1218745, 371293 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Obtained by evaluating the half-exponential generating function D(x,y) in Lemma 3.1 of Drmota et al. D(x,y) = sum_{n,m} d_(n,m)*x^n*y^m/n! with log( (1+D)/(1+y)) = x*D^2/(1+x*D). The diagonal appears to be A052750. LINKS Michael Drmota, Omer Gimenez, Marc Noy, Vertices of given degree in series-parallel graphs, Rand. Struct. Algo. 36 (3) (2010) 273-314 EXAMPLE The table d_(n,m) [which is T(n,m) with leading zeros maintained] for the number of SP networks with n+2 vertices and m nodes (internal nodes labeled from 1 to n) starts in row n=0 with columns m>=0 as: n\m| 0  1  2  3  4 ---------------------- 0  | 0  1 1  | 0  0  1  1 2  | 0  0  0  2  7  5 3  | 0  0  0  0  6 48  91  49 CROSSREFS Sequence in context: A151856 A019825 A097157 * A195450 A079833 A198737 Adjacent sequences:  A181317 A181318 A181319 * A181321 A181322 A181323 KEYWORD tabl,nonn AUTHOR R. J. Mathar, Jan 26 2011 STATUS approved

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