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A163774
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Row sums of the central coefficients triangle (A163771).
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1
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1, 3, 13, 51, 201, 783, 3039, 11763, 45481, 175803, 679779, 2630367, 10187659, 39500373, 153329913, 595883763, 2318471289, 9030982491
(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} sum{i=k..n} (-1)^(n-i)*binomial(n-k,n-i)*(2i)$
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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MAPLE
| swing := proc(n) option remember; if n = 0 then 1 elif
irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:
a := proc(n) local i, k; add(add((-1)^(n-i)*binomial(n-k, n-i)*swing(2*i), i=k..n), k=0..n) end:
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CROSSREFS
| Cf. A163771.
Sequence in context: A026529 A101052 A016064 * A197074 A014985 A015521
Adjacent sequences: A163771 A163772 A163773 * A163775 A163776 A163777
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KEYWORD
| nonn
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 05 2009
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