A268557 Number of immersions of unoriented circle into oriented sphere with n labeled double points, where additionally each double point distinguishes one of the 4 half-edges incident to it.

2, 32, 1344, 99840, 11034624, 1646100480, 311739678720, 71904311377920, 19608902534430720, 6183679018118676480, 2216537535694661222400, 890848169343849804595200, 397015474116844831585075200, 194397347759742363293555097600, 103774855190390649524854141747200

Offset

1,1

Links

Table of n, a(n) for n=1..15.

R. Coquereaux and J.-B. Zuber, Maps, immersions and permutations, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), DOI: 10.1142/S0218216516500474.

Formula

a(n) = A268567(n) * 4^n / 2 [proof: a (2*4^(n-1))-to-one map to the labeled immersions of an oriented circle is can be defined e.g. by choosing the orientation of the circle along the distinguished half-edge of the vertex #1]. - Andrey Zabolotskiy, Jan 14 2025

Crossrefs

Cf. A268567.

Sequence in context: A012214 A320419 A012140 * A281183 A012209 A295418

Adjacent sequences: A268554 A268555 A268556 * A268558 A268559 A268560

Keyword

nonn,changed

Author

N. J. A. Sloane, Mar 02 2016

Extensions

New name and terms a(7) onwards from Andrey Zabolotskiy, Jan 21 2025

Status

approved