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 A383569 #12 Aug 09 2025 13:52:48
%S A383569 1,0,2,0,6,0,20,1,70,6,252,30,924,140,3433,630,12882,2772,48710,12012,
%T A383569 185316,51481,708582,218810,2720788,923990,10484684,3881556,40528441,
%U A383569 16236486,157086660,67675972,610318610,281236620,2376289056,1165715161,9269869182
%N A383569 Expansion of 1/sqrt((1-x^7)^2 - 4*x^2).
%C A383569 Number of lattice paths from (0,0) to (n,n) using steps (2,0),(0,2),(7,7).
%C A383569 Diagonal of the rational function 1 / (1 - x^2 - y^2 - x^7*y^7).
%C A383569 Diagonal of the rational function 1 / ((1-x^2*y)*(1-x^5*y^6) - y).
%H A383569 R. A. Sulanke, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/SULANKE/sulanke.html">Moments of generalized Motzkin paths</a>, J. Integer Sequences, Vol. 3 (2000), #00.1.
%t A383569 CoefficientList[Series[1/Sqrt[(1-x^7)^2-4x^2],{x,0,40}],x] (* _Harvey P. Dale_, Aug 09 2025 *)
%o A383569 (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x^7)^2-4*x^2))
%Y A383569 Cf. A002426, A053442, A383568.
%K A383569 nonn
%O A383569 0,3
%A A383569 _Seiichi Manyama_, Apr 30 2025