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A128890
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Triangle T(n,k) related to walks in the positive quadrant .
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0
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1, 0, 1, 2, 0, 1, 0, 5, 0, 1, 10, 0, 9, 0, 1, 0, 35, 0, 14, 0, 1, 70, 0, 84, 0, 20, 0, 1, 0, 294, 0, 168, 0, 27, 0, 1, 588, 0, 840, 0, 300, 0, 35, 0, 1, 0, 2772, 0, 1980, 0, 495, 0, 44, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| T(n,k)=binomial(n,r)*binomial(n+2,s)-binomial(n+2,r+1)*binomial(n,s-1)with r=(n+k)/2 and s=(n-k)/2, if n+k is even ; else T(n,k)=0 . T(2*n,0)=A000108(n)*A000108(n+1)=A005568(n) .
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EXAMPLE
| Triangle begins:
1;
0, 1;
2, 0, 1;
0, 5, 0, 1;
10, 0, 9, 0, 1;
0, 35, 0, 14, 0, 1;
70, 0, 84, 0, 20, 0, 1;
0, 294, 0, 168, 0, 27, 0, 1;
588, 0, 840, 0, 300, 0, 35, 0, 1;
0, 2772, 0, 1980, 0, 495, 0, 44, 0, 1;
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CROSSREFS
| Cf. A000012, A000096, A052472, A005568, A000356.
Sequence in context: A132277 A137286 A180048 * A196777 A078924 A137526
Adjacent sequences: A128887 A128888 A128889 * A128891 A128892 A128893
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 20 2007
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