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Search: id:A094385
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| A094385 |
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Another version of triangular array in A062991 unsigned and transposed : triangle T(n,k), 0<=k<=n, read by rows; given by [0, 1, 1, 1, 1, 1, 1, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938. |
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+0
5
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| 1, 0, 1, 0, 1, 2, 0, 2, 6, 5, 0, 5, 20, 28, 14, 0, 14, 70, 135, 120, 42, 0, 42, 252, 616, 770, 495, 132, 0, 132, 924, 2730, 4368, 4004, 2002, 429, 0, 429, 3432, 11880, 23100, 27300, 19656, 8008, 1430, 0, 1430, 12870, 51051, 116688, 168300, 157080, 92820, 31824
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Diagonals : A000007, A000108, 2*A001700; A000108, A002694 . Row sums : A064092 (generalized Catalan C(2; n)
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REFERENCES
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B. Derrida, E. Domany and D. Mukamel, A 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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FORMULA
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Sum_{k = 0..n} T(n, k)*x^(n-k) = C(x+1; n), generalized Catalan numbers; see left diagonals of triangle A064094 : A000012, A000108, A064062-63, A064087-93 for x = -1, 0, .., 9, respectively.
T(n,0)=0^n, T(n,k)=binomial(2*n,k-1)*binomial(2*n-k-1,n-k)/n for n>=1 and k>=1 .
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 2;
0, 2, 6, 5;
0, 5, 20, 28, 14;
0, 14, 70, 135, 120, 42;
0, 42, 252, 616, 770, 495, 132;
0, 132, 924, 2730, 4368, 4004, 2002, 429;
0, 429, 3432, 11880, 23100, 27300, 19656, 8008, 1430 ;...
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CROSSREFS
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Sequence in context: A033757 A136426 A157491 this_sequence A156815 A161803 A057980
Adjacent sequences: A094382 A094383 A094384 this_sequence A094386 A094387 A094388
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 03 2004, Jun 14 2007
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