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 A062985 #12 Jan 05 2025 19:51:36
%S A062985 1,1,1,1,1,1,1,2,3,4,5,5,5,5,5,1,3,6,10,15,20,25,30,35,35,35,35,35,1,
%T A062985 4,10,20,35,55,80,110,145,180,215,250,285,285,285,285,285,1,5,15,35,
%U A062985 70,125,205,315,460,640,855,1105
%N A062985 Generalized Catalan array FS(5; n,r).
%C A062985 In the Frey-Sellers reference this array is called {n over r}_{m-1}, with m=5.
%C A062985 The step width sequence of this staircase array is [1,4,4,4,....], i.e. the degree of the row polynomials is [0,4,8,12,...]= A008586.
%C A062985 The columns r=0..7 (without leading zeros) give A000012 (powers of 1), A000027 (natural), A000217 (triangular), A000292 (tetrahedral), A000332(4+n), A062988-A062990.
%H A062985 D. D. Frey and J. A. Sellers, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/39-2/frey.pdf">Generalizing Bailey's generalization of the Catalan numbers</a>, The Fibonacci Quarterly, 39 (2001) 142-148.
%F A062985 a(0, 0)=1, a(n, -1)=0, n >= 1; a(n, r)=0 if r>4*n; a(n, r)=a(n, r-1)+a(n-1, r) else.
%F A062985 G.f. for column r=4*k+j, k >= 0, j=1, 2, 3, 4: (x^(k+1))*N(5; k, x)/(1-x)^(4*k+1+j), with row polynomials of array A062986.
%e A062985 {1}; {1,1,1,1,1}; {1,2,3,4,5,5,5,5,5}; ...; N(5; 1,x)=5-10*x+10*x^2-5*x^3+x^4.
%K A062985 nonn,easy,tabf
%O A062985 0,8
%A A062985 _Wolfdieter Lang_, Jul 12 2001