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A131427
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A000108(n) preceded by n zeros.
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6
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1, 0, 1, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 429, 0, 0, 0, 0, 0, 0, 0, 0, 1430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58786, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208012
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OFFSET
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0,6
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COMMENTS
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T(n,k) is the number of Dyck paths of semilength n having exactly k U=(1,1) steps. - Alois P. Heinz, Jun 09 2014
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LINKS
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FORMULA
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A000108(n) preceded by n zeros, as an infinite lower triangular matrix.
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EXAMPLE
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First few rows of the triangle are:
1;
0, 1;
0, 0, 2;
0, 0, 0, 5;
0, 0, 0, 0, 14;
0, 0, 0, 0, 0, 42;
...
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MAPLE
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T:= (n, k)-> `if`(k<n, 0, binomial(2*n, n)/(n+1)):
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MATHEMATICA
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T[n_, n_] := CatalanNumber[n]; T[_, _] = 0;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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