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A163842
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Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial transform. Same as interpolating the beta numbers 1/beta(n,n) (A002457) with (A163869).
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5
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1, 7, 6, 43, 36, 30, 249, 206, 170, 140, 1395, 1146, 940, 770, 630, 7653, 6258, 5112, 4172, 3402, 2772, 41381, 33728, 27470, 22358, 18186, 14784, 12012, 221399, 180018, 146290, 118820, 96462, 78276, 63492
(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} 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
| Peter Luschny, Swinging Factorial.
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EXAMPLE
| 1
7, 6
43, 36, 30
249, 206, 170, 140
1395, 1146, 940, 770, 630
7653, 6258, 5112, 4172, 3402, 2772
41381, 33728, 27470, 22358, 18186, 14784, 12012
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MAPLE
| Computes n rows of the triangle. For the functions 'SumTria' and 'swing' see A163840.
a := n -> SumTria(k->swing(2*k+1), n, true);
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CROSSREFS
| Sum rows are A163845. Cf. A056040, A163650, A163841, A163842, A163840, A002426, A000984.
Sequence in context: A163260 A073112 A070425 * A038272 A130553 A002394
Adjacent sequences: A163839 A163840 A163841 * A163843 A163844 A163845
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KEYWORD
| nonn,tabl
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 06 2009
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