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Search: id:A109450
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| A109450 |
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Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938. |
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+0
2
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| 1, 0, 1, 0, 1, 2, 0, 1, 5, 5, 0, 1, 8, 20, 14, 0, 1, 11, 44, 75, 42, 0, 1, 14, 77, 208, 275, 132, 0, 1, 17, 119, 440, 910, 1001, 429, 0, 1, 20, 170, 798, 2244, 3808, 3640, 1430, 0, 1, 23, 230, 1309, 4655, 10659, 15504, 13260, 4862, 0, 1, 26, 299, 2000
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Row sums : 1, 1, 3, 11, 43, 173, .... (see A026671).
Transposed version in A107842.
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FORMULA
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T(0, 0) = 1, T(n, 0) = 0 if n>0, T(n, k) = 0 if k>n, T(n, k) = (3n-3k+2)*binomial(3n-k-1, k-1)/(3n-2k+1).
T(n, n) = A000108(n), Catalan numbers.
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 2;
0, 1, 5, 5;
0, 1, 8, 20, 14;
0, 1, 11, 44, 75, 42;
0, 1, 14, 77, 208, 275, 132
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CROSSREFS
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Cf. A000108, A000344, A003518, A000589, A107842.
Sequence in context: A004491 A004483 A085650 this_sequence A086810 A085838 A094456
Adjacent sequences: A109447 A109448 A109449 this_sequence A109451 A109452 A109453
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 26 2005
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