This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268567 #13 Jan 22 2025 00:06:20 %S A268567 1,4,42,780,21552,803760,38054160,2194345440,149604053760, %T A268567 11794431720960,1056927459571200,106197377365094400, %U A268567 11831983152533913600,1448373107312190259200,193295730632526147225600,27939600631552720061952000,4349183288219555957563392000 %N A268567 Number of immersions of oriented circle into oriented sphere with n labeled double points. %H A268567 R. Coquereaux and J.-B. Zuber, <a href="https://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), DOI: <a href="https://doi.org/10.1142/S0218216516500474">10.1142/S0218216516500474</a>. %F A268567 a(n) = A054993(n)*(n-1)!/2 [proof: in a long curve, label the first (leftmost) crossing by #1 and the rest by whatever, in (n-1)! ways; then each labeled oriented spherical closed curve corresponds to precisely 2 such labeled long curves, depending on which of the 2 edges going into vertex #1 is chosen to be "long"]. - _Andrey Zabolotskiy_, Jan 14 2025 %Y A268567 Cf. A054993, A264755, A008986. %K A268567 nonn %O A268567 1,2 %A A268567 _N. J. A. Sloane_, Mar 03 2016 %E A268567 New name and terms a(11) onwards from _Andrey Zabolotskiy_, Jan 21 2025