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Search: id:A113206
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| A113206 |
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Triangle read by rows of generalized Catalan numbers. |
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+0
1
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| 1, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 3, 5, 3, 0, 1, 1, 0, 4, 12, 14, 12, 4, 0, 1, 1, 0, 5, 22, 55, 42, 55, 22, 5, 0, 1, 1, 0, 6, 35, 140, 273, 132, 273, 140, 35, 6, 0, 1, 1, 0, 7, 51, 285, 969, 1428, 429, 1428, 969, 285, 51, 7, 0, 1, 1, 0, 8, 70, 506, 2530, 7084, 7752, 1430, 7752, 7084
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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A dual to Pascal's triangle. Row n has 2n+1 entries.
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REFERENCES
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Ph. Leroux, A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers, arXiv:math.CO/0512437.
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FORMULA
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T(n,k) = A070914(n-|n-k|-1,|n-k|+1) if 3<=k<=2n-3 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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EXAMPLE
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.............1
...........1.0.1
.........1.0.2.0.1
.......1.0.3.5.3.0.1
....1.0.4.12.14.12.4.0.1
.1.0.5.22.55.42.55.22.5.0.1
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MAPLE
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A070914 := proc(n, k) binomial(n*(k+1), n)/(n*k+1) ; end: A113206 := proc(n, k) if k = 2 or k = 2*n-2 then 0 ; else A070914(n-abs(n-k)-1, abs(n-k)+1) ; fi ; end: for n from 0 to 10 do for k from 1 to 2*n-1 do printf("%d ", A113206(n, k)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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CROSSREFS
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Cf. A007318, A000108.
Sequence in context: A049310 A036851 A036850 this_sequence A158800 A144024 A075107
Adjacent sequences: A113203 A113204 A113205 this_sequence A113207 A113208 A113209
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 07 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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