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A163772
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Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial inverse.
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5
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1, 5, 6, 19, 24, 30, 67, 86, 110, 140, 227, 294, 380, 490, 630, 751, 978, 1272, 1652, 2142, 2772, 2445, 3196, 4174, 5446, 7098, 9240, 12012, 7869, 10314, 13510, 17684, 23130, 30228, 39468, 51480
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Triangle read by rows. For n >= 0, k >= 0 let
T(n,k) = sum{i=k..n} (-1)^(n-i)*binomial(n-k,n-i)*(2i+1)$
where i$ denotes the swinging factorial of i (A056040).
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REFERENCES
| Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
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LINKS
| M. Z. Spivey and L. L. Steil, The k-Binomial Transforms and the Hankel Transform, J. Integ. Seqs. Vol. 9 (2006), #06.1.1.
Peter Luschny, Swinging Factorial.
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EXAMPLE
| 1
5, 6
19, 24, 30
67, 86, 110, 140
227, 294, 380, 490, 630
751, 978, 1272, 1652, 2142, 2772
2445, 3196, 4174, 5446, 7098, 9240, 12012
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MAPLE
| For the functions 'DiffTria' and 'swing' see A163770. Computes n rows of the triangle.
a := n -> DiffTria(k->swing(2*k+1), n, true);
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CROSSREFS
| Sum rows are A163775. Cf. A056040, A163650, A163771, A163772, A002426, A000984.
Sequence in context: A056519 A063445 A031448 * A056509 A129722 A133608
Adjacent sequences: A163769 A163770 A163771 * A163773 A163774 A163775
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KEYWORD
| nonn,tabl
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 05 2009
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