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A130743
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Triangle related to super-Catalan numbers (or little Schroeder numbers).
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0
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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 .
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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 ;...
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CROSSREFS
| Sequence in context: A202560 A173933 A193821 * A206455 A111574 A173590
Adjacent sequences: A130740 A130741 A130742 * A130744 A130745 A130746
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 12 2007
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