A278992 - OEIS

%I #29 Nov 03 2021 06:03:39

%S 0,1,1,21,168,1968,26094,398653,6872377,132050271,2798695656,

%T 64866063276,1632224748984,44316286165297,1291392786926821,

%U 40202651019430461,1331640833909877144,46762037794122159492,1735328399106396110310,67858430028772637693845

%N Number of simple chord-labeled chord diagrams with n chords.

%H E. Krasko and A. Omelchenko, <a href="http://arxiv.org/abs/1601.05073">Enumeration of Chord Diagrams without Loops and Parallel Chords</a>, arXiv preprint arXiv:1601.05073 [math.CO], 2016.

%H E. Krasko and A. Omelchenko, <a href="https://doi.org/10.37236/6037">Enumeration of Chord Diagrams without Loops and Parallel Chords</a>, The Electronic Journal of Combinatorics, 24(3) (2017), #P3.43.

%F E.g.f.: (1+sqrt(1-2*t))*(1-2*t)^(-1/2)*exp(-1-t+sqrt(1-2*t))-(2-t)*exp(-t).

%F a(n) ~ 2^(n+1/2) * n^n / exp(n+3/2). - _Vaclav Kotesovec_, Dec 07 2016

%F Conjecture D-finite with recurrence: +(-n+2)*a(n) +(2*n^2-8*n+7)*a(n-1) +(6*n^2-18*n+11)*a(n-2) +(n-1)*(6*n-11)*a(n-3) +2*(n-1)*(n-2)*a(n-4)=0. - _R. J. Mathar_, Jan 27 2020

%t terms = 20;

%t CoefficientList[(Sqrt[1 - 2t]+1)(1/Sqrt[1 - 2t])*E^(Sqrt[1 - 2t] - t - 1) - (2-t)/E^t + O[t]^(terms+1), t]*Range[0, terms]! // Rest (* _Jean-François Alcover_, Sep 14 2018 *)

%Y Cf. A003436, A003437, A007474, A278990, A278991, A278993, A278994.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Dec 07 2016