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 A372878 #14 May 17 2024 01:42:30
%S A372878 1,7,33,133,496,1770,6142,20902,70107,232489,763927,2491107,8071234,
%T A372878 26007364,83402988,266351548,847482277,2687729595,8499036925,
%U A372878 26804655025,84336597636,264777690382,829636763338,2594821366338,8102197327711,25259791668925,78638974063827
%N A372878 a(n) is the sum of all symmetric valleys in the set of flattened Catalan words of length n.
%C A372878 The g.f. listed in Baril et al. has a mistake in the numerator: the factor (1 + 2*x) should be (1 - 2*x).
%H A372878 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. 18.
%H A372878 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,46,-33,9).
%F A372878 From Baril et al.: (Start)
%F A372878 G.f.: x^4*(1 - 2*x)/((1 - 3*x)^2*(1 - x)^3).
%F A372878 a(n) = (3^n*(2*n - 5) - 18*n^2 + 54*n - 27)/144. (End)
%F A372878 E.g.f.: (32 + exp(3*x)*(6*x - 5) - 9*exp(x)*(2*x^2 - 4*x + 3))/144.
%F A372878 a(n) - a(n-1) = A261064(n-3).
%t A372878 LinearRecurrence[{9,-30,46,-33,9},{1,7,33,133,496},28]
%Y A372878 Cf. A261064, A371963, A371964, A372875.
%K A372878 nonn,easy
%O A372878 4,2
%A A372878 _Stefano Spezia_, May 15 2024