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Search: id:A163841
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| A163841 |
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Triangle interpolating the swinging factorial (A056040) restricted to even indices with its binomial transform. Same as interpolating bilateral Schroeder paths (A026375) with the central binomial coefficients (A000984). |
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4
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| 1, 3, 2, 11, 8, 6, 45, 34, 26, 20, 195, 150, 116, 90, 70, 873, 678, 528, 412, 322, 252, 3989, 3116, 2438, 1910, 1498, 1176, 924, 18483, 14494, 11378, 8940, 7030, 5532, 4356, 3432, 86515, 68032, 53538
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Triangle read by rows. For n >= 0, k >= 0 let
T(n,k) = sum{i=k..n} binomial(n-k,n-i)*(2i)$
where i$ denotes the swinging factorial of i (A056040).
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REFERENCES
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Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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LINKS
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Peter Luschny, Swinging Factorial.
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EXAMPLE
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1
3, 2
11, 8, 6
45, 34, 26, 20
195, 150, 116, 90, 70
873, 678, 528, 412, 322, 252
3989, 3116, 2438, 1910, 1498, 1176, 924
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MAPLE
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Computes n rows of the triangle. For the functions 'SumTria' and 'swing' see A163840.
a := n -> SumTria(k->swing(2*k), n, true);
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CROSSREFS
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Sum rows are A163844. Cf. A056040, A163650, A163841, A163842, A163840, A026375, A002426, A000984.
Sequence in context: A013945 A065014 A072656 this_sequence A072634 A086194 A159610
Adjacent sequences: A163838 A163839 A163840 this_sequence A163842 A163843 A163844
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KEYWORD
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nonn,tabl
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Aug 06 2009
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