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A096465
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Triangle (read by rows) formed by setting all entries in the first column and in the main diagonal ((i,i) entries) to 1 and the rest of the entries by the recursion a(n,m) = a(n-1,m) + a(n,m-1).
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1
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1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 8, 9, 1, 1, 5, 13, 22, 23, 1, 1, 6, 19, 41, 64, 65, 1, 1, 7, 26, 67, 131, 196, 197, 1, 1, 8, 34, 101, 232, 428, 625, 626, 1, 1, 9, 43, 144, 376, 804, 1429, 2055, 2056, 1, 1, 10, 53, 197, 573, 1377, 2806, 4861, 6917, 6918, 1, 1, 11, 64, 261, 834
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| The third column is A034856 (C(n + 1, 2) + n - 1.) The row sums are A014137 (partial sums of Catalan numbers (A000108)). The "first subdiagonal" ((i+1,i) entries) are also A014137. The "2nd subdiagonal" ((i+2,i) entries) is A014138 ( Partial sums of Catalan numbers (starting 1,2,5,...).) The "3rd subdiagonal" ((i+3,i) entries) is A001453 (Catalan numbers - 1.)
This is the reverse of A091491 - see A091491 for more information. The sequence of antidiagonal sums gives A124642. - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Dec 09 2006
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CROSSREFS
| Cf. A034856, A014137, A014138, A001453, A000108.
Cf. A091491, A024718, A006134, A078478, A100066, A105848, A124642.
Sequence in context: A197957 A089899 A092422 * A124460 A144042 A122084
Adjacent sequences: A096462 A096463 A096464 * A096466 A096467 A096468
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KEYWORD
| nonn,tabl
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AUTHOR
| Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Aug 12 2004
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