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 A263841 #31 Jan 26 2024 16:12:17
%S A263841 1,3,9,28,87,271,843,2619,8123,25153,77763,240054,740017,2278329,
%T A263841 7006093,21520872,66039651,202462113,620164491,1898109900,5805127269,
%U A263841 17741909157,54188530641,165405964227,504601360389,1538559689751,4688812503053,14282580916834,43486805133903
%N A263841 Expansion of (1 - 2*x - x^2)/(sqrt(1+x)*(1-3*x)^(3/2)*2*x) - 1/(2*x).
%H A263841 A. Asinowski and G. Rote, <a href="http://arxiv.org/abs/1502.04925">Point sets with many non-crossing matchings</a>, arXiv preprint arXiv:1502.04925 [cs.CG], 2015. See Table 1.
%F A263841 D-finite with recurrence: -(n+1)*(n^2+n-3)*a(n) + 2*(n^3+3*n^2-4*n-3)*a(n-1) + 3*(n-1)*(n^2+3*n-1)*a(n-2) = 0. - _R. J. Mathar_, Feb 17 2016
%F A263841 From _Mélika Tebni_, Jan 24 2024: (Start)
%F A263841 a(n) = A005773(n+1) + A132894(n).
%F A263841 E.g.f.: (1+x)*exp(x)*(BesselI(0,2*x) + BesselI(1,2*x)). (End)
%F A263841 From _Mélika Tebni_, Jan 25 2024: (Start)
%F A263841 a(n) = Sum_{k=0..n} A189911(k)*binomial(n,k).
%F A263841 a(n) = Sum_{k=0..n} (k+1)*binomial(n,k)*binomial(n-k,floor((n-k)/2)). (End)
%p A263841 A263841 := n -> add((k+1)*binomial(n, k)*binomial(n-k, iquo(n-k,2)), k = 0 .. n):
%p A263841 seq(A263841(n), n = 0 .. 28); # _Mélika Tebni_, Jan 25 2024
%t A263841 CoefficientList[Series[(1-2x-x^2)/(Sqrt[1+x] (1-3x)^(3/2) 2x)-1/(2x),{x,0,30}],x] (* _Harvey P. Dale_, Aug 21 2017 *)
%o A263841 (PARI) my(x='x+O('x^40)); Vec((1-2*x-x^2)/(sqrt(1+x)*(1-3*x)^(3/2)*2*x)-1/(2*x)) \\ _Altug Alkan_, Nov 10 2015
%Y A263841 Cf. A005773, A132894, A189911.
%K A263841 nonn
%O A263841 0,2
%A A263841 _N. J. A. Sloane_, Nov 02 2015