A130743 - OEIS

%I #4 Sep 08 2013 13:31:20

%S 1,1,1,2,3,3,4,8,11,11,8,20,34,45,45,16,48,96,152,197,197,32,112,256,

%T 464,706,903,903,64,256,656,1328,2276,3376,4279,4279,128,576,1632,

%U 3632,6856,11332,16514,20793,20793,256,1280,3968,9600,19680,35488,57184

%N Triangle related to super-Catalan numbers (or little Schroeder numbers).

%F T(n,k)=Sum_{m,j,m<n,j<=k}T(m,j), T(0,0)=1, T(n,k)=0 if k<0 or if k>n . T(n,n)=A001003(n) . T(n,0)=A011782(n). T(n,1)=A001792(n-1) for n>=1 . T(n,2)=A084266(n-1) for n>=2 .

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 3, 3;

%e 4, 8, 11, 11;

%e 8, 20, 34, 45, 45;

%e 16, 48, 96, 152, 197, 197;

%e 32, 112, 256, 464, 706, 903, 903:

%e 64, 256, 656, 1328, 2276, 3376, 4279, 4279;

%e 128, 576, 1632, 3632, 6856, 11332, 16514, 20793, 20793 ;...

%K nonn,tabl

%O 0,4

%A _Philippe Deléham_, Jul 12 2007