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 A353133 #14 May 20 2022 08:58:15
%S A353133 1,5,16,47,136,392,1130,3262,9434,27337,79364,230815,672380,1961635,
%T A353133 5730860,16763685,49093260,143924943,422352816,1240529133,3646710456,
%U A353133 10728322770,31584554610,93048320820,274292367650,809044988695,2387642856380,7050001551361,20826624824612,61552574382856
%N A353133 Coefficients of expansion of f(x) = (1+x*m(x))^5*(x^2*(x*m(x))'+1) where m(x) is the generating function for A001006.
%C A353133 2*x^7*f(x) is the generating function for the number of Dyck paths with L(D)=7 where L(D) is the product of binomial coefficients (u_i(D)+d_i(D) choose u_i(D)), where u_i(D) is the number of up-steps between the i-th and (i+1)-st down step and d_i(D) is the number of down-steps between the i-th and (i+1)-st up step.
%H A353133 Kassie Archer and Christina Graves, <a href="https://arxiv.org/abs/2104.12664">Pattern-restricted permutations composed of 3-cycles</a>, arXiv:2104.12664 [math.CO], 2021.
%H A353133 Kassie Archer and Christina Graves, <a href="https://arxiv.org/abs/2205.09686">A new statistic on Dyck paths for counting 3-dimensional Catalan words</a>, arXiv:2205.09686 [math.CO], 2022.
%o A353133 (PARI) m(x) = (1-x-sqrt(1-2*x-3*(x^2)))/(2*(x^2));
%o A353133 my(x='x+O('x^30)); Vec((1+x*m(x))^5*(x^2*(x*m(x))'+1)) \\ _Michel Marcus_, Apr 25 2022
%Y A353133 Cf. A001006, A005717, A005773, A025565, A225034.
%K A353133 nonn
%O A353133 0,2
%A A353133 _Kassie Archer_, Apr 25 2022