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 A383568 #12 Apr 30 2025 09:13:57
%S A383568 1,0,2,0,6,1,20,6,70,30,253,140,936,630,3522,2773,13430,12032,51770,
%T A383568 51690,201389,220470,789546,935330,3116416,3951949,12373910,16645398,
%U A383568 49389050,69938416,198048409,293296470,797461358,1228136090,3222960100,5136602753
%N A383568 Expansion of 1/sqrt((1-x^5)^2 - 4*x^2).
%C A383568 Number of lattice paths from (0,0) to (n,n) using steps (2,0),(0,2),(5,5).
%C A383568 Diagonal of the rational function 1 / (1 - x^2 - y^2 - x^5*y^5).
%C A383568 Diagonal of the rational function 1 / ((1-x^2*y)*(1-x^3*y^4) - y).
%H A383568 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.
%o A383568 (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x^5)^2-4*x^2))
%Y A383568 Main diagonal of A383567.
%Y A383568 Cf. A002426, A053442, A383569.
%K A383568 nonn
%O A383568 0,3
%A A383568 _Seiichi Manyama_, Apr 30 2025