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 A372852 #9 May 17 2024 01:39:42
%S A372852 1,3,10,35,123,427,1460,4923,16405,54131,177150,575731,1860047,
%T A372852 5978715,19131880,60982859,193710249,613415779,1937102450,6101872707,
%U A372852 19177314211,60147030923,188286357660,588394867675,1835791987133,5719198113747,17793060798310,55285581766163
%N A372852 a(n) is the total number of runs of ascents over all flattened Catalan words of length n.
%H A372852 Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, <a href="https://arxiv.org/abs/2405.05357">Flattened Catalan Words</a>, arXiv:2405.05357 [math.CO], 2024. See p. 7.
%H A372852 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,24,-9).
%F A372852 From Baril et al.: (Start)
%F A372852 G.f.: x*(1 - 5*x + 8*x^2 - 3*x^2)/((1 - x)^2*(1 - 3*x)^2).
%F A372852 a(n) = (3^(n-1) + 1)*(n + 1)/4. (End)
%F A372852 E.g.f.: exp(x)*(exp(2*x) - 1)*(x - 2)/4.
%t A372852 LinearRecurrence[{8,-22,24,-9},{1,3,10,35},28]
%Y A372852 Cf. A007051, A372868, A372872.
%K A372852 nonn,easy
%O A372852 1,2
%A A372852 _Stefano Spezia_, May 15 2024