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 A337902 #7 Sep 29 2020 12:15:00 %S A337902 3,50,735,10584,152460,2208492,32207175,472780880,6982113996, %T A337902 103673813880,1546866469148,23179817220000,348690679038000, %U A337902 5263441096145400,79698007774092375,1210159553338375200,18422202264818467500,281089726445607849000 %N A337902 The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (2,1). %F A337902 a(n) = binomial(2*n+1,n-1)*binomial(2*n+1,n) = A002054(n)*A001700(n). %F A337902 G.f.: 3*x*3F2(2,5/2,5/2; 3,4; 16*x). %F A337902 D-finite with recurrence (n-1)*(n+2)*(n+1)*a(n) -4*n*(2*n+1)^2*a(n-1)=0. %F A337902 A135389(n) = 2*A060150(n+1) +2*a(n). %e A337902 a(1)=3 represents 3 walks of length 3: RRU, URR and RUR. %Y A337902 Cf. A002894 (at (0,0)), A060150 (at (1,0)), A135389 (at (1,1)), A337900 (at (2,0)), A337901 (at (3,0)) %K A337902 nonn,easy,walk %O A337902 1,1 %A A337902 _R. J. Mathar_, Sep 29 2020