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A117513
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Number of ways of arranging 2n tokens in a row, with 2 copies of each token from 1 through n, such that between every pair of tokens labeled i (i=1..n-1) there is exactly one taken labeled i+1.
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3
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1, 2, 12, 136, 2480, 66336, 2446528, 118984832, 7378078464, 568142287360, 53189920492544, 5949749335001088, 783686338494312448, 120058889459865165824, 21166245289132322242560
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution from Paul Barry (pbarry(AT)wit.ie), Oct 12 2009: (Start)
The aerated sequence is a(n)=(2^(n/2-1)+0^(n/2)/2)*((1+(-1)^n)/2)*n!*[x^n](1+x*tan(x/2)).
Multiples of the unsigned Genocchi numbers A110501: (1,1,3,17,155,...)*(1,2,4,8,16,...) (End)
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
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FORMULA
| G.f.: 1/(1-2x/(1-4x/(1-8x/(1-12x/(1-18x/(1-24x/(1-32x/(1-.../(1-2*floor((n+2)^2/4)*x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Dec 03 2009]
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CROSSREFS
| Cf. A002105, A117514, A117515.
Sequence in context: A201561 A205886 A108996 * A185522 A119819 A093543
Adjacent sequences: A117510 A117511 A117512 * A117514 A117515 A117516
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KEYWORD
| nonn
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AUTHOR
| Nan Zang (nzang(AT)cs.ucsd.edu), Apr 28 2006
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EXTENSIONS
| More terms from Paul Barry (pbarry(AT)wit.ie), Oct 12 2009
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