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A050157
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T(n,k)=S(2n,n,k), 0<=k<=n, n >= 0, where S(p,q,r)=number of upright paths from (0,0) to (p,p-q) that do not rise above the line y=x-r.
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10
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1, 1, 2, 2, 5, 6, 5, 14, 19, 20, 14, 42, 62, 69, 70, 42, 132, 207, 242, 251, 252, 132, 429, 704, 858, 912, 923, 924, 429, 1430, 2431, 3068, 3341, 3418, 3431, 3432, 1430, 4862, 8502, 11050, 12310, 12750, 12854, 12869, 12870
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let V=(e(1),...,e(n)) consist of q 1's and p-q 0's; let V(h)=(e(1),...,e(h)) and m(h)=(#1's in V(h))-(#0's in V(h)) for h=1,...,n. Then S(p,q,r)=number of V having r>=max{m(h)}.
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FORMULA
| T(n, k)=Sum{t(n, j): 0<=j<=k}, array t as in A039599.
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EXAMPLE
| Rows: {1}; {1,2}; {2,5,6}; ...
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CROSSREFS
| Sequence in context: A176989 A112573 A120406 * A054255 A063177 A034803
Adjacent sequences: A050154 A050155 A050156 * A050158 A050159 A050160
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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