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 A372872 #8 May 17 2024 01:40:33
%S A372872 1,2,6,20,67,222,728,2368,7653,24602,78730,250956,797159,2524342,
%T A372872 7971612,25110584,78918985,247518642,774840974,2421378052,7554699531,
%U A372872 23535794702,73222472416,227512682160,706073841197,2188828907722,6778308875538,20970393083708,64817578622383
%N A372872 a(n) is the total number of runs of weak ascents over all flattened Catalan words of length n.
%H A372872 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. 10.
%H A372872 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,24,-9).
%F A372872 From Baril et al.: (Start)
%F A372872 G.f.: x*(1 - 2*x)^3/(1 - 4*x + 3*x^2)^2.
%F A372872 a(n) = (27 - 9*n + (5 + n)*3^n)/36. (End)
%F A372872 E.g.f.: (exp(3*x)*(5 + 3*x) - 9*exp(x)*(x - 3) - 32)/36.
%t A372872 LinearRecurrence[{8,-22,24,-9},{1,2,6,20},29]
%Y A372872 Cf. A372852, A372868.
%K A372872 nonn,easy
%O A372872 1,2
%A A372872 _Stefano Spezia_, May 15 2024