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 A054394 #17 Oct 16 2018 03:56:37
%S A054394 1,1,2,5,14,42,132,429,1429,4847,16660,57820,202086,709928,2503266,
%T A054394 8850681,31355020,111242127,395091069,1404332528,4994581900,
%U A054394 17771328588,63253477326,225194224134,801884971816,2855809269782,10171707099565
%N A054394 Number of permutations with certain forbidden subsequences.
%H A054394 E. Barcucci et al., <a href="http://dx.doi.org/10.1016/S0012-365X(99)00254-X">From Motzkin to Catalan Permutations</a>, Discr. Math., 217 (2000), 33-49.
%H A054394 Nickolas Hein, Jia Huang, <a href="https://arxiv.org/abs/1807.04623">Variations of the Catalan numbers from some nonassociative binary operations</a>, arXiv:1807.04623 [math.CO], 2018.
%F A054394 Conjecture: g.f.(x)=1+z*(1-2z+z^2-z^3)/(1-3z+3z^2-3z^3+2z^4-z^5) where z=x*A001006(x) and A001006(x) is the g.f. of A001006. [_R. J. Mathar_, Jul 07 2009]
%t A054394 a[0] = 1; a[n_] := Module[{M}, M = Table[If[j < i || i == j && i <= 6 || j == i+1, 1, 0], {i, 1, n}, {j, 1, n}]; MatrixPower[M, n][[1, 1]]];
%t A054394 Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, Aug 16 2018, after A054391 *)
%Y A054394 Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108). Cf. A005773, A054391-A054393.
%K A054394 nonn
%O A054394 0,3
%A A054394 _N. J. A. Sloane_, Elisa Pergola (elisa(AT)dsi.unifi.it), May 21 2000