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 A062750 #13 Jan 05 2025 19:51:36
%S A062750 1,1,1,1,1,1,2,3,4,4,4,4,1,3,6,10,14,18,22,22,22,22,1,4,10,20,34,52,
%T A062750 74,96,118,140,140,140,140,1,5,15,35,69,121,195,291,409,549,689,829,
%U A062750 969,969,969,969,1,6,21,56,125
%N A062750 Generalized Catalan array FS(4; n,r).
%C A062750 In the Frey-Sellers reference this array is called {n over r}_{m-1}, with m=4.
%C A062750 The step width sequence of this staircase array is [1,3,3,3,....], i.e. the degree of the row polynomials is [0,3,6,9,...]= A008585.
%C A062750 The columns r=0..6 give A000012 (powers of 1), A000027 (natural), A000217 (triangular), A000292 (tetrahedral), A063258, A027659, A062966.
%H A062750 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 A062750 a(0, 0)=1, a(n, -1)=0, n >= 1; a(n, r)=0 if r>3*n; a(n, r)=a(n, r-1)+a(n-1, r) else.
%F A062750 G.f. for column r=3*k+j, k >= 0, j=1, 2, 3: (x^(k+1))*N(4; k, x)/(1-x)^(3*k+1+j), with the row polynomials N(4; k, x) of array A062751.
%e A062750 {1}; {1,1,1,1}; {1,2,3,4,4,4,4}; {1,3,6,10,14,18,22,22,22,22}; ...; N(4; 1,x)=(2-x)*(2-2*x+x^2).
%K A062750 nonn,easy,tabf
%O A062750 0,7
%A A062750 _Wolfdieter Lang_, Jul 12 2001