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A163865
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The binomial transform of the swinging factorial (A056040).
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2
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1, 2, 5, 16, 47, 146, 447, 1380, 4251, 13102, 40343, 124136, 381625, 1172198, 3597401, 11031012, 33798339, 103477590, 316581567, 967900224, 2957316429, 9030317478, 27558851565, 84059345244, 256265811333
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = sum {k=0..n} binomial(n,k) k$, where k$ denotes the swinging factorial of k (A056040). The swinging analog to the number of arrangements, the binomial transform of the factorial (A000522).
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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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MAPLE
| a := proc(n) local k: add(binomial(n, k)*(k!/iquo(k, 2)!^2), k=0..n) end:
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CROSSREFS
| Cf. A056040, A000522, A163650.
Sequence in context: A075887 A148376 A148377 * A148378 A148379 A148380
Adjacent sequences: A163862 A163863 A163864 * A163866 A163867 A163868
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KEYWORD
| nonn
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 06 2009
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