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%I #8 Jul 24 2013 01:13:40
%S 1,1,1,2,7,5,6,48,91,49,24,360,1304,1697,729,120,3000,17910,41440,
%T 41051,14641,720,27720,249900,899730,1524282,1218745,371293
%N Triangle T(n,m) read by rows: the number of series-parallel networks with n+2 vertices and m+n+1 edges.
%C Obtained by evaluating the half-exponential generating function D(x,y) in Lemma 3.1 of Drmota et al.
%C 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).
%C The diagonal appears to be A052750.
%H Michael Drmota, Omer Gimenez, Marc Noy, <a href="http://dx.doi.org/10.1002/rsa.20290">Vertices of given degree in series-parallel graphs</a>, Rand. Struct. Algo. 36 (3) (2010) 273-314
%e 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:
%e n\m| 0 1 2 3 4
%e ----------------------
%e 0 | 0 1
%e 1 | 0 0 1 1
%e 2 | 0 0 0 2 7 5
%e 3 | 0 0 0 0 6 48 91 49
%K tabl,nonn
%O 0,4
%A _R. J. Mathar_, Jan 26 2011