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A163872
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Inverse binomial transform of the beta numbers 1/beta(n+1,n+1) (A002457).
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1
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1, 5, 19, 67, 227, 751, 2445, 7869, 25107, 79567, 250793, 786985, 2460397, 7667921, 23832931, 73902627, 228692115, 706407903, 2178511449, 6708684009
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also a(n) = sum {i=0..n} (-1)^(n-i) binomial(n,n-i) (2*i+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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FORMULA
| o.g.f A(x)=1/(1-x*M(x))^3, M(x) - o.g.f A001006. a(n):=sum(k^3/n*sum(binomial(n,j)*binomial(j,2*j-n-k),j,0,n),k,1,n); [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 06 2010]
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MAPLE
| a := proc(n) local i; add((-1)^(n-i)*binomial(n, i)/Beta(i+1, i+1), i=0..n) end:
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CROSSREFS
| Cf. A163772.
Sequence in context: A005021 A067325 A121525 * A035344 A114277 A104496
Adjacent sequences: A163869 A163870 A163871 * A163873 A163874 A163875
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KEYWORD
| nonn
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 06 2009
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