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 A248324 #29 Nov 11 2024 03:57:05 %S A248324 1,3,6,18,9,45,126,36,45,360,945,189,135,270,2970,7371,1134,567,648, %T A248324 1782,24948,58968,7371,2835,2268,3564,12474,212058,480168,50544,15795, %U A248324 9720,10692,21384,90882,1817640,3961386,360126,94770,47385,40095,56133,136323,681615,15677145,33011550,2640924,600210,252720,173745,187110,318087,908820,5225715,135868590 %N A248324 Square array read by antidiagonals downwards: super Patalan numbers of order 3. %C A248324 Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 3, A097188. %H A248324 Thomas M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv:1410.5880 [math.CO], 2014. %H A248324 Thomas M. Richardson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Richardson/rich2.html">The Super Patalan Numbers</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.3. %F A248324 T(0,0)=1, T(n,k) = T(n-1,k)*(9*n-3)/(n+k), T(n,k) = T(n,k-1)*(9*k-6)/(n+k). %F A248324 G.f.: (x/(1-9*x)^(2/3)+y/(1-9*y)^(1/3))/(x+y-9*x*y). %e A248324 T(0..4,0..4) is: %e A248324 1 3 18 126 945 %e A248324 6 9 36 189 1134 %e A248324 45 45 135 567 2835 %e A248324 360 270 648 2268 9720 %e A248324 2970 1782 3564 10692 40095 %Y A248324 Cf. A068555, A248325. First column is A004988, first row is A004987. a(n,1) = -A004990(n+1) = 3*A097188(n). a(1,k) = -A004989(k+1). %K A248324 tabl,easy,nonn %O A248324 0,2 %A A248324 _Tom Richardson_, Oct 04 2014