Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #25 Nov 11 2024 03:56:52
%S 1,6,30,126,90,990,3276,1260,1980,33660,93366,24570,20790,50490,
%T 1161270,2800980,560196,324324,424116,1393524,40412196,86830380,
%U 14004900,6162156,5513508,9754668,40412196,1414426860,2753763480,372130200,132046200,89791416,108694872,242473176,1212365880
%N Square array read by antidiagonals downwards: super Patalan numbers of order 6.
%C Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 6, A025751.
%H Thomas M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv:1410.5880 [math.CO], 2014.
%H 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 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 G.f.: (x/(1-36*x)^(5/6)+y/(1-36*y)^(1/6))/(x+y-36*x*y).
%F T(n,k) = (-1)^k*36^(n+k)*binomial(n-1/6,n+k).
%e T(0..4,0..4) is
%e 1 6 126 3276 93366
%e 30 90 1260 24570 560196
%e 990 1980 20790 324324 6162156
%e 33660 50490 424116 5513508 89791416
%e 1161270 1393524 9754668 108694872 1548901926
%o (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 Cf. A068555, A025751, A004993 (first row), A004994 (first column), A004995 (second row), A004996 (second column), A248324, A248325, A248326, A248329, A248332.
%K nonn,tabl,easy
%O 0,2
%A _Tom Richardson_, Oct 04 2014