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%I #13 Jul 11 2017 04:39:21
%S 1,1,1,1,2,1,1,2,3,1,1,2,4,4,1,1,3,6,7,5,1,1,3,7,10,11,6,1,1,3,9,13,
%T 17,16,7,1,1,4,11,16,27,28,22,8,1,1,4,13,22,37,44,44,29,9,1,1,4,15,24,
%U 49,64,72,66,37,10,1,1,5,18,32,66,85,116,116,95,46,11,1
%N Triangular array: T(n,k) gives the number of numerical semigroups of genus n and multiplicity k, (n>=1, k>=2).
%C A numerical semigroup is a subset S of N, the nonnegative integers, that is closed under addition, contains the element 0 and such that N-S is finite. The cardinality of N-S is called the genus of S. The least positive integer belonging to S is called the multiplicity of S. The number of numerical semigroups of genus n is A007323(n).
%H V. Blanco, P. A. Garcia-Sanchez and J. Puerto, <a href="http://arXiv.org/abs/0901.1228">Computing the number of numerical semigroups using generating functions</a>, arXiv:0901.1228v3 [math.CO], 2009.
%H Nathan Kaplan, <a href="https://arxiv.org/abs/1707.02551">Counting Numerical Semigroups</a>, arXiv:1707.02551 [math.CO], 2017.
%e Triangle begins
%e .n\k.|..2....3....4....5....6....7....8....9...10
%e = = = = = = = = = = = = = = = = = = = = = = = = =
%e ..1..|..1
%e ..2..|..1....1
%e ..3..|..1....2....1
%e ..4..|..1....2....3....1
%e ..5..|..1....2....4....4....1
%e ..6..|..1....3....6....7....5....1
%e ..7..|..1....3....7...10...11....6....1
%e ..8..|..1....3....9...13...17...16....7....1
%e ..9..|..1....4...11...16...27...28...22....8....1
%e ...
%e T(3,3) = 2: The two numerical semigroups of genus 3 and multiplicity 3 are S = N - {1,2,4} and S = N - {1,2,5}.
%Y Cf. A007323 (row sums).
%K nonn,tabl
%O 1,5
%A _Peter Bala_, Nov 09 2011
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