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A024255
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a(0)=0, a(n) = n*E(2n-1) for n>=1, where E(n) = A000111(n) are the Euler (or up-down) numbers.
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2
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0, 1, 4, 48, 1088, 39680, 2122752, 156577792, 15230058496, 1888788086784, 290888851128320, 54466478584365056, 12185086638082228224, 3209979242472703787008, 983522422455215438430208
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of cyclically alternating permutations of length 2n. Example: a(2)=4 because we have 1324, 1423, 2314, and 2413 (3412 is alternating but not cyclically alternating).
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REFERENCES
| N. D. Elkies, On the sums Sum_{k = -infinity .. infinity} (4k+1)^(-n), Amer. Math. Monthly, 110 (No. 7, 2003), 561-573.
G. Kreweras, Les preordres totaux compatibles avec un ordre partiel. Math. Sci. Humaines No. 53 (1976), 5-30.
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LINKS
| N. D. Elkies, On the sums Sum((4k+1)^(-n),k,-inf,+inf)
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FORMULA
| a(n) = 2^(n-1)*(2^n-1)*|B_n|.
G.f.: tan(x)*x/2.
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MAPLE
| a := n -> (-1)^n*2^(2*n-1)*(1-2^(2*n))*bernoulli(2*n); [From Peter Luschny (peter(AT)luschny.de), Jun 08 2009]
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MATHEMATICA
| Tan[x]*x/2 (* Even Part *)
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CROSSREFS
| Cf. A009752.
Sequence in context: A138448 A071221 A198038 * A166231 A191952 A013145
Adjacent sequences: A024252 A024253 A024254 * A024256 A024257 A024258
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KEYWORD
| nonn
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 01 2009
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