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 A065058 #16 Dec 12 2015 04:18:17 %S A065058 1,1,3,18,162,1851,24661,365613,5863881,99895425,1785024645, %T A065058 33156724734,635961987570,12531882072719,252701147866029, %U A065058 5198011293931270,108793300411597194,2312049376195527621,49804793378882733343,1085910951385068915212,23934948368968158240960 %N A065058 Number of paths to T(n,n,n) with T(i,j,k)= 0 if j>i or k>j and T(i,j,k) = T(i-1,j,k) + T(i,j-1,k) + T(i,j,k-1) and T(i,j,0) = 1. %C A065058 Similar to the "3-dimensional Catalan numbers" of A005789, but with paths starting from anywhere on z=0, instead of only from [0,0,0]. %H A065058 Alois P. Heinz, <a href="/A065058/b065058.txt">Table of n, a(n) for n = 0..500</a> %F A065058 a(n) ~ 13 * 3^(3*n+7/2) / (2^11 * Pi * n^4). - _Vaclav Kotesovec_, Sep 10 2014 %e A065058 a(3) = 18 because [3,3,3] can be reached from [x,y,0] in the following ways (along nondecreasing paths): 5 [1,1,0] + 5 [2,1,0] + 3 [2,2,0] + 2 [3,1,0] + 2 [3,2,0] + [3,3,0]. %t A065058 T[0, 0, 0] := 1; T[x_, y_, z_] := 0 /; (x< y || y< z); T[u_, v_, 0] := 1; T[_, 0, 0] := 1 T[x_, y_, z_] := (T[x, y, z]= T[x-1, y, z]+T[x, y-1, z] +T[x, y, z-1]) /; (y<=x ||z<=y) %Y A065058 Cf. A005789. %K A065058 nonn %O A065058 0,3 %A A065058 _Wouter Meeussen_, Nov 06 2001