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A181320
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Triangle T(n,m) read by rows: the number of series-parallel networks with n+2 vertices and m+n+1 edges.
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0
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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
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..27.
Michael Drmota, Omer Gimenez, Marc Noy, Vertices of given degree in series-parallel graphs, Rand. Struct. Algo. 36 (3) (2010) 273-314
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EXAMPLE
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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
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0 | 0 1
1 | 0 0 1 1
2 | 0 0 0 2 7 5
3 | 0 0 0 0 6 48 91 49
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CROSSREFS
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Sequence in context: A151856 A019825 A097157 * A195450 A079833 A198737
Adjacent sequences: A181317 A181318 A181319 * A181321 A181322 A181323
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KEYWORD
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tabl,nonn
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AUTHOR
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R. J. Mathar, Jan 26 2011
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STATUS
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approved
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