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Search: id:A101475
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| A101475 |
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Triangle T(n,k) read by rows: number of lattice paths from (0,0) to (0,2n) with steps (1,1) or (1,-1) that stay between the lines y=0 and y=k. |
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+0
2
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| 1, 1, 2, 3, 5, 6, 10, 15, 19, 20, 35, 50, 63, 69, 70, 126, 176, 217, 243, 251, 252, 462, 638, 770, 870, 913, 923, 924, 1716, 2354, 2794, 3159, 3355, 3419, 3431, 3432, 6435, 8789, 10307, 11610, 12430, 12766, 12855, 12869, 12870, 24310, 33099, 38489
(list; table; graph; listen)
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OFFSET
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0,3
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LINKS
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W.Y.C. Cheng, E.Y.P. Deng, R.R.X. Du, R. P. Stanley and C. H. Yan, Crossings and nestings of matchings and partitions
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FORMULA
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T(n, k) = Sum[i>=0, C(2n, n-i(k+2))-C(2n, n+i(k+2)+k+1) ].
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EXAMPLE
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1
1,2
3,5,6
10,15,19,20
35,50,63,69,70
126,176,217,243,251,252
462,638,770,870,913,923,924
1716,2354,2794,3159,3355,3419,3431,3432
6435,8789,10307,11610,12430,12766,12855,12869,12870
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CROSSREFS
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Left-hand columns include A001700 and A024718. Right-hand columns include A000984 and A030662. Row sums are in A101476.
Sequence in context: A039845 A039848 A018494 this_sequence A018524 A057035 A018594
Adjacent sequences: A101472 A101473 A101474 this_sequence A101476 A101477 A101478
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Jan 21 2005
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