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%I #68 Mar 30 2024 12:17:55
%S 1,1,2,6,19,76,376,2194,14614,106421,823832,6657811,55557329,
%T 475475046,4155030702,36959470662,333860366236
%N Number of immersions of an unoriented circle into the unoriented sphere with n double points.
%D V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 18.
%H J. Cantarella, H. Chapman, and M. Mastin, <a href="https://arxiv.org/abs/1512.05749">Knot Probabilities in Random Diagrams</a>, arXiv preprint arXiv:1512.05749 [math.GT], 2015. Also Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 40 (2016), DOI: 10.1088/1751-8113/49/40/405001
%H R. Coquereaux and J.-B. Zuber, <a href="http://arxiv.org/abs/1507.03163">Maps, immersions and permutations</a>, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), <a href="http://dx.doi.org/10.1142/S0218216516500474">10.1142/S0218216516500474</a>.
%H Guy Valette, <a href="https://doi.org/10.1007/s40598-016-0049-3">A Classification of Spherical Curves Based on Gauss Diagrams</a>, Arnold Math J. (2016) 2:383-405.
%e G.f. = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 76*x^5 + 376*x^6 + 2194*x^7 + ...
%o (Magma) // see A260914
%Y Cf. A008986, A008987, A008988, A264759, A277739. First line of triangle A260914.
%K nonn,more
%O 0,3
%A _N. J. A. Sloane_
%E a(6)-a(7) from _Guy Valette_, Feb 09 2004
%E a(8)-a(9) from _Robert Coquereaux_ and Jean-Bernard Zuber, Jul 21 2015
%E a(10) from same source added by _N. J. A. Sloane_, Mar 03 2016
%E a(11)-a(14) from _Brendan McKay_, Mar 11 2023
%E a(15)-a(16) from _Brendan McKay_, Mar 29 2024