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 A366774 #28 Jan 04 2024 12:17:30
%S A366774 1,1,2,5,15,52,203,876,4115,20765,111301,627821,3698873,22623354,
%T A366774 142940629,929208778,6194162081,42223649277,293640007995,
%U A366774 2079196943605,14964254850197,109308213994757,809340696014733,6067405789245061,46008536947670701,352579939415882813
%N A366774 Number of 2-distant 3-noncrossing partitions of {1,...,n}.
%C A366774 a(n+1) is the binomial transform of A108304.
%D A366774 Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, Discrete Math. 343 (2020), no. 6, 111705, 5 pp.
%H A366774 Jean-François Alcover, <a href="/A366774/b366774.txt">Table of n, a(n) for n = 0..200</a>
%H A366774 Juan B. Gil and Jordan O. Tirrell, <a href="https://arxiv.org/abs/1806.09065">A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions</a>, arXiv:1806.09065 [math.CO], 2018-2023.
%F A366774 a(n+1) = Sum_{i=0..n} binomial(n,i)*A108304(i).
%F A366774 a(n) ~ 2^(n+1) * 5^(n+7) / (3^(9/2) * Pi * n^7). - _Vaclav Kotesovec_, Jan 04 2024
%e A366774 There are 877 partitions of 7 elements, but a(7)=876 because the partition (1,5)(2,6)(3,7)(4) has a 2-distant 3-crossing.
%t A366774 b[n_] := b[n] = If[n < 2, 1, (2*(5*n^2 + 12*n - 2)*b[n - 1] + 9*(-n^2 + n + 2)*b[n - 2])/((n + 4)*(n + 5))];
%t A366774 a[n_] := If[n == 0, 1, Sum[Binomial[n - 1, i]*b[i], {i, 0, n - 1}]];
%t A366774 Table[a[n], {n, 0, 200}] (* _Jean-François Alcover_, Nov 25 2023 *)
%Y A366774 Cf. A108304, A366775, A366776.
%K A366774 nonn
%O A366774 0,3
%A A366774 _Juan B. Gil_, Nov 13 2023
%E A366774 More terms from _Jean-François Alcover_, Nov 25 2023