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 A053442 #32 Apr 30 2025 09:14:01
%S A053442 1,0,2,1,6,6,21,30,82,141,342,650,1485,2982,6612,13693,29922,63072,
%T A053442 136905,291618,631302,1353441,2928054,6303798,13642117,29454702,
%U A053442 63791456,138020533,299191968,648376932,1406836717,3052671816,6629649798,14400972413,31301837952
%N A053442 Moments of generalized Motzkin paths.
%C A053442 From _Seiichi Manyama_, Apr 30 2025: (Start)
%C A053442 Number of lattice paths from (0,0) to (n,n) using steps (2,0),(0,2),(3,3).
%C A053442 Diagonal of the rational function 1 / (1 - x^2 - y^2 - x^3*y^3).
%C A053442 Diagonal of the rational function 1 / ((1-x^2*y)*(1-x*y^2) - y). (End)
%H A053442 Michael De Vlieger, <a href="/A053442/b053442.txt">Table of n, a(n) for n = 0..2917</a>
%H A053442 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.
%F A053442 G.f.: 1 / sqrt(1-4*z^2-2*z^3+z^6). - _Sean A. Irvine_, Dec 25 2021
%t A053442 CoefficientList[Series[1/Sqrt[1 - 4 x^2 - 2 x^3 + x^6], {x, 0, 34}], x], (* _Michael De Vlieger_, Dec 25 2021 *)
%o A053442 (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1-4*x^2-2*x^3+x^6)) \\ _Seiichi Manyama_, Apr 30 2025
%Y A053442 Cf. A002426.
%K A053442 nonn,easy,nice
%O A053442 0,3
%A A053442 _N. J. A. Sloane_, Jan 12 2000
%E A053442 More terms from _Reiner Martin_, Oct 13 2002
%E A053442 Typos in terms corrected by _Sean A. Irvine_, Dec 25 2021
%E A053442 Offset changed to 0 by _Seiichi Manyama_, Apr 30 2025