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 A337292 #30 Aug 10 2025 08:19:30
%S A337292 5,20,130,1020,8855,81900,791120,7887660,80560285,838553320,
%T A337292 8863227100,94871786100,1026317094705,11203116342560,123243929011680,
%U A337292 1364973221797900,15207477517956825,170321264840835900,1916512328325665070,21655893753689280120
%N A337292 a(n) = 4*binomial(5*n,n)/(5*n-1).
%C A337292 a(n) is the number of lattice paths from (0,0) to (4n,n) using only the steps (1,0) and (0,1) and whose only lattice points on the line y = x/4 are the path's endpoints.
%F A337292 a(n) = 5*A118971(n-1).
%F A337292 G.f.: 5*x*F(x)^4 where F(x) = 1 + x*F(x)^5 is the g.f. of A002294.
%F A337292 D-finite with recurrence 8*n*(4*n-3)*(2*n-1)*(4*n-1)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-6)*a(n-1)=0., a(0)=1. - _R. J. Mathar_, Jan 26 2025
%F A337292 G.f.: -4*4F3(-1/5,1/5,2/5,3/5; 1/4,1/2,3/4; 3125*x/256) . - _R. J. Mathar_, Aug 10 2025
%t A337292 Array[4 Binomial[5 #, #]/(5 # - 1) &, 20] (* _Michael De Vlieger_, Aug 21 2020 *)
%o A337292 (PARI) a(n) = {4*binomial(5*n,n)/(5*n-1)} \\ _Andrew Howroyd_, Aug 21 2020
%Y A337292 Cf. A002294, A118971, A337291.
%K A337292 nonn,easy
%O A337292 1,1
%A A337292 _Lucas A. Brown_, Aug 21 2020