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%I #17 Apr 25 2019 09:31:01
%S 1,1,2,3,3,6,8,7,15,20,18,36,44,45,83,109,101,174,246,227
%N Number of symmetric numerical semigroups with Frobenius number 2*n-1; that is, symmetric numerical semigroups for which the largest integer not belonging to them is 2*n-1.
%H CombOS - Combinatorial Object Server, <a href="http://combos.org/sgroup.html">Generate numerical semigroups</a>
%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Monoids of natural numbers</a>
%H S. R. Finch, <a href="/A066062/a066062.pdf">Monoids of natural numbers</a>, March 17, 2009. [Cached copy, with permission of the author]
%H J. C. Rosales, P. A. Garcia-Sanchez, J. I. Garcia-Garcia and J. A. Jimenez-Madrid, <a href="https://doi.org/10.1016/j.jpaa.2003.10.024">Fundamental gaps in numerical semigroups</a>, Journal of Pure and Applied Algebra 189 (2004) 301-313.
%H Clayton Cristiano Silva, <a href="http://www.ime.unicamp.br/~ftorres/ENSINO/MONOGRAFIAS/Clayton.pdf">Irreducible Numerical Semigroups</a>, University of Campinas, São Paulo, Brazil (2019).
%F a(n) = A158206(2*n-1).
%e a(3)=2: the only 2 symmetric semigroups with Frobenius number 5=2*3-1 are generated by {3, 4} and {2, 7}.
%Y Cf. A124506, A158206.
%K nonn,more
%O 1,3
%A _Steven Finch_, Mar 15 2009