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A118976
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Triangle read by rows: T(n,k)=binomial(n-1,k-1)*binomial(n,k-1)/k + binomial(n-1,k)*binomial(n,k)/(k+1) (1<=k<=n). In other words, to each entry of the Narayana triangle (A001263) add the entry on its right.
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1
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1, 2, 1, 4, 4, 1, 7, 12, 7, 1, 11, 30, 30, 11, 1, 16, 65, 100, 65, 16, 1, 22, 126, 280, 280, 126, 22, 1, 29, 224, 686, 980, 686, 224, 29, 1, 37, 372, 1512, 2940, 2940, 1512, 372, 37, 1, 46, 585, 3060, 7812, 10584, 7812, 3060, 585, 46, 1, 56, 880, 5775, 18810, 33264
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sum of entries in row n=2*Cat(n)-1, where Cat(n) are the Catalan numbers (A000108).
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FORMULA
| Row sums = A131428 starting (1, 3, 9, 27, 83,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 31 2007
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EXAMPLE
| First few rows of the triangle are:
(1);
(2, 1);
(4, 4, 1);
(7, 12, 7, 1);
(11, 30, 30, 11, 1);
(16, 65, 100, 65, 16, 1);
...
Row 4 of the triangle = (7, 12, 7, 1), derived from row 4 of the Narayana triangle, (1, 6, 6, 1): = ((1+6), (6+6), (6+1), (1)).
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MAPLE
| T:=(n, k)->binomial(n-1, k-1)*binomial(n, k-1)/k+binomial(n-1, k)*binomial(n, k)/(k+1): for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A001263, A034856.
Cf. A000108.
Cf. A131428.
Sequence in context: A013609 A154558 A008572 * A138177 A101559 A122438
Adjacent sequences: A118973 A118974 A118975 * A118977 A118978 A118979
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 07 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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