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 A248328 #25 Nov 11 2024 03:56:52 %S A248328 1,6,30,126,90,990,3276,1260,1980,33660,93366,24570,20790,50490, %T A248328 1161270,2800980,560196,324324,424116,1393524,40412196,86830380, %U A248328 14004900,6162156,5513508,9754668,40412196,1414426860,2753763480,372130200,132046200,89791416,108694872,242473176,1212365880 %N A248328 Square array read by antidiagonals downwards: super Patalan numbers of order 6. %C A248328 Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 6, A025751. %H A248328 Thomas M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv:1410.5880 [math.CO], 2014. %H A248328 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 A248328 T(0,0)=1, T(n,k) = T(n-1,k)*(36*n-6)/(n+k), T(n,k) = T(n,k-1)*(36*k-30)/(n+k). %F A248328 G.f.: (x/(1-36*x)^(5/6)+y/(1-36*y)^(1/6))/(x+y-36*x*y). %F A248328 T(n,k) = (-1)^k*36^(n+k)*binomial(n-1/6,n+k). %e A248328 T(0..4,0..4) is %e A248328 1 6 126 3276 93366 %e A248328 30 90 1260 24570 560196 %e A248328 990 1980 20790 324324 6162156 %e A248328 33660 50490 424116 5513508 89791416 %e A248328 1161270 1393524 9754668 108694872 1548901926 %o A248328 (PARI) matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*36^(n+k)*binomial(n-1/6,n+k)) \\ _Michel Marcus_, Oct 09 2014 %Y A248328 Cf. A068555, A025751, A004993 (first row), A004994 (first column), A004995 (second row), A004996 (second column), A248324, A248325, A248326, A248329, A248332. %K A248328 nonn,tabl,easy %O A248328 0,2 %A A248328 _Tom Richardson_, Oct 04 2014