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A034928
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Triangle of ballot numbers.
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0
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1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 4, 1, 1, 4, 6, 9, 9, 1, 1, 5, 8, 15, 21, 21, 1, 1, 6, 10, 22, 36, 51, 51, 1, 1, 7, 12, 30, 54, 91, 127, 127, 1, 1, 8, 14, 39, 75, 142, 232, 323, 323, 1, 1, 9, 16, 49, 99, 205, 370, 603, 835, 835, 1, 1, 10, 18, 60, 126, 281, 545
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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REFERENCES
| M. Aigner, Motzkin Numbers, Europ. J. Comb. 19 (1998), 663-675.
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FORMULA
| a(0, 0)=a(0, 1)=1, a(n, n+1)=a(n, n), a(n, k)=a(n-1, 0)+...+a(n-1, k-2)+a(n-1, k) (n >= 1, 0<=k<=n).
Or, from David W. Wilson: a(n, 0) = 1; a(n, 1) = 1; a(n, 2) = n; a(n, k) = 0 if k > n+1; a(n, k) = a(n-1, k) + a(n, k-1) + a(n-1, k-2) - a(n-1, k-1), otherwise.
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EXAMPLE
| 1 1; 1 1 1; 1 1 2 2; 1 1 3 4 4;...
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CROSSREFS
| Sequence in context: A146565 A115594 A086623 * A161671 A144444 A054106
Adjacent sequences: A034925 A034926 A034927 * A034929 A034930 A034931
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net).
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