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Search: id:A162470
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| A162470 |
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Table read by rows: the Catalan number C(n) followed by pairs (C(n-1-j), C(j+1)), j=0 to n-2. |
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1
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| 1, 2, 1, 1, 5, 2, 1, 1, 2, 5, 14, 5, 1, 2, 2, 1, 5, 42, 14, 1, 5, 2, 2, 5, 1, 14, 132, 42, 1, 14, 2, 5, 5, 2, 14, 1, 42, 429, 132, 1, 42, 2, 14, 5, 5, 14, 2, 42, 1, 132, 1430, 429, 1, 132, 2, 42, 5, 14, 14, 5, 42, 2, 132, 1, 429, 4862, 1430, 1, 429, 2, 132, 5, 42, 14, 14, 42, 5, 132, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The table starts row n with A000108(n) = C(n) and then visualizes
the convolution formula C(n) = sum_{j=0..n-1} C(j)*C(n-1-j) by listing some
pairs of that structure in the same row.
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EXAMPLE
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Starting in row n=1 the table reads
1;
2,1,1;
5,2,1,1,2;
14,5,1,2,2,1,5;
42,14,1,5,2,2,5,1,14;
132,42,1,14,2,5,5,2,14,1,42;
The row n=3 represents 5=2*1+1*1+1*2, for example, where the middle term is not represented in the table.
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CROSSREFS
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cf. A000108.
Sequence in context: A136789 A022661 A120292 this_sequence A128604 A098885 A106270
Adjacent sequences: A162467 A162468 A162469 this_sequence A162471 A162472 A162473
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KEYWORD
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nonn,tabf,less
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 04 2009
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EXTENSIONS
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Definition and comment rephrased by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 16 2009
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