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A070914
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Array read by antidiagonals giving number of paths up and left from (0,0) to (n,kn) where x/y<=k for all intermediate points.
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4
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 5, 1, 1, 1, 4, 12, 14, 1, 1, 1, 5, 22, 55, 42, 1, 1, 1, 6, 35, 140, 273, 132, 1, 1, 1, 7, 51, 285, 969, 1428, 429, 1, 1, 1, 8, 70, 506, 2530, 7084, 7752, 1430, 1, 1, 1, 9, 92, 819, 5481, 23751, 53820, 43263, 4862, 1, 1, 1, 10, 117, 1240
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Also related to dissections of polygons and enumeration of trees.
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FORMULA
| T(n, k) =C(n*(k+1), n)/(n*k+1) =A071201(n, kn) =A071201(n, kn+1) =A071202(n, kn+1) =A062993(n+k-1, k-1)
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EXAMPLE
| Rows start 1,1,1,1,1,1,...; 1,1,1,1,1,1,...; 1,2,3,4,5,6,...; 1,5,12,22,35,51,...; 1,14,55,140,285,506,...; etc.
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CROSSREFS
| Rows include A000012 (twice), A000027, A000326. Columns include A000012, A000108 (Catalan), A001764, A002293, A002294, A002295, A002296, A007556, A062994, A062744.
Reflected version of A062993 (which is the main entry).
Sequence in context: A140075 A099555 A124530 * A144150 A124560 A201949
Adjacent sequences: A070911 A070912 A070913 * A070915 A070916 A070917
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 20 2002
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