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A130020
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Triangle T(n,k), 0<=k<=n, read by rows given by [1,0,0,0,0,0,0,...] DELTA [0,1,1,1,1,1,1,...] where DELTA is the operator defined in A084938 .
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18
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1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 5, 0, 1, 4, 9, 14, 14, 0, 1, 5, 14, 28, 42, 42, 0, 1, 6, 20, 48, 90, 132, 132, 0, 1, 7, 27, 75, 165, 297, 429, 429, 0, 1, 8, 35, 110, 275, 572, 1001, 1430, 1430, 0, 1, 9, 44, 154, 429, 1001, 2002, 3432, 4862, 4862, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Reflected version of A106566 .
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FORMULA
| Sum_{k, 0<=k<=n}T(n,k)=A000108(n).
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EXAMPLE
| Triangle begins:
1;
1, 0;
1, 1, 0;
1, 2, 2, 0;
1, 3, 5, 5, 0;
1, 4, 9, 14, 14, 0;
1, 5, 14, 28, 42, 42, 0;
1, 6, 20, 48, 90, 132, 132, 0;
1, 7, 27, 75, 165, 297, 429, 429, 0;
1, 8, 35, 110, 275, 572, 1001, 1430, 1430, 0;
1, 9, 44, 154, 429, 1001, 2002, 3432, 4862, 4862, 0 ;...
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CROSSREFS
| 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: A144064 A172236 A191646 * A091063 A198793 A085388
Adjacent sequences: A130017 A130018 A130019 * A130021 A130022 A130023
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 16 2007
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