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A030237
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Catalan's triangle with right border removed: 1; 1,2; 1,3,5; ...
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20
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1, 1, 2, 1, 3, 5, 1, 4, 9, 14, 1, 5, 14, 28, 42, 1, 6, 20, 48, 90, 132, 1, 7, 27, 75, 165, 297, 429, 1, 8, 35, 110, 275, 572, 1001, 1430, 1, 9, 44, 154, 429, 1001, 2002, 3432, 4862
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history;
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OFFSET
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0,3
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COMMENTS
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This triangle appears in the totally asymmetric exclusion process as Y(alpha=1,beta=1,n,m), written in the Derrida et al. reference as Y_n(m) for alpha=1, beta=1. - Wolfdieter Lang, Jan 13 2006.
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REFERENCES
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B. Derrida, E. Domany and D. Mukamel, An exact solution of a one-dimensional asymmetric exclusion model with open boundaries, J. Stat. Phys. 69, 1992, 667-687; eqs. (20), (21), p. 672.
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LINKS
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Reinhard Zumkeller, Rows n=0..150 of triangle, flattened
W. Lang: First 10 rows.
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FORMULA
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m-th entry in row n is (n+m)!/n!/m! /(n+1) (n-m+1).
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PROG
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(Haskell)
a030237 n k = a030237_tabl !! n !! k
a030237_row n = a030237_tabl !! n
a030237_tabl = map init $ tail a009766_tabl
-- Reinhard Zumkeller, Jul 12 2012
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CROSSREFS
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Cf. A009766.
Row sums give A071724(n)= 3*binomial(2*n, n-1)/(n+2), n>=1.
The following are all versions of (essentially) the same Catalan triangle: A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.
Diagonals give A000108 A000245 A002057 A000344 A003517 A000588 A003518 A003519 A001392, ...
Sequence in context: A188211 A175009 A049069 * A210557 A118243 A210233
Adjacent sequences: A030234 A030235 A030236 * A030238 A030239 A030240
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KEYWORD
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nonn,tabl
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AUTHOR
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Wouter Meeussen.
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EXTENSIONS
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Missing a(8) = T(7,0) = 1 inserted by Reinhard Zumkeller, Jul 12 2012
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STATUS
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approved
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