A130743 Triangle related to super-Catalan numbers (or little Schroeder numbers).

1, 1, 1, 2, 3, 3, 4, 8, 11, 11, 8, 20, 34, 45, 45, 16, 48, 96, 152, 197, 197, 32, 112, 256, 464, 706, 903, 903, 64, 256, 656, 1328, 2276, 3376, 4279, 4279, 128, 576, 1632, 3632, 6856, 11332, 16514, 20793, 20793, 256, 1280, 3968, 9600, 19680, 35488, 57184

Offset

0,4

Links

Table of n, a(n) for n=0..51.

Formula

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 .

Example

Triangle begins:
1;
1, 1;
2, 3, 3;
4, 8, 11, 11;
8, 20, 34, 45, 45;
16, 48, 96, 152, 197, 197;
32, 112, 256, 464, 706, 903, 903:
64, 256, 656, 1328, 2276, 3376, 4279, 4279;
128, 576, 1632, 3632, 6856, 11332, 16514, 20793, 20793 ;...

Crossrefs

Sequence in context: A173933 A351407 A193821 * A263775 A206455 A227263

Adjacent sequences: A130740 A130741 A130742 * A130744 A130745 A130746

Keyword

nonn,tabl

Author

Philippe Deléham, Jul 12 2007

Status

approved