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A091836
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A triangle of Motzkin ballot numbers.
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1
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1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 4, 6, 6, 4, 1, 9, 13, 13, 10, 5, 1, 21, 30, 30, 24, 15, 6, 1, 51, 72, 72, 59, 40, 21, 7, 1, 127, 178, 178, 148, 105, 62, 28, 8, 1, 323, 450, 450, 378, 276, 174, 91, 36, 9, 1, 835, 1158, 1158, 980, 730, 480, 273, 128, 45, 10, 1, 2188, 3023, 3023
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Mirror image of A034929. Column k has g.f. z^k(1+zM)^(k+1). T(n,0)=A086246(n+1)=A001006(n-1). T(n,1)=A05554(n). Row sums are the Motzkin numbers (A001006).
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REFERENCES
| M. Aigner, Motzkin numbers, Europ. J. Comb., 19 (1998), 663-675.
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LINKS
| J.-C. Novelli and J.-Y. Thibon, Noncommutative Symmetric Functions and Lagrange Inversion
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FORMULA
| G.f.=(1+zM)/[1-tz(1+zM)], where M=1+zM+z^2M^2 is the g.f. of the Motzkin numbers (A001006).
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EXAMPLE
| [1], [1, 1], [1, 2, 1], [2, 3, 3, 1], [4, 6, 6, 4, 1], [9, 13, 13, 10, 5, 1], [21, 30, 30, 24, 15, 6, 1], ...
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CROSSREFS
| Cf. A001006, A086246, A005554, A034929.
Sequence in context: A099569 A191579 A097724 * A080850 A109449 A129570
Adjacent sequences: A091833 A091834 A091835 * A091837 A091838 A091839
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 09 2004
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