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A025164
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a(n) = a(n-2)+(2n-1)a(n-1); a(0)=1, a(1)=1.
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3
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1, 4, 21, 151, 1380, 15331, 200683, 3025576, 51635475, 984099601, 20717727096, 477491822809, 11958013297321, 323343850850476, 9388929687961125, 291380164177645351, 9624934347550257708, 337164082328436665131
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Numerator of continued fraction given by C(n) = [ 1;3,5,7,...(2n-1)]. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 02 2001
Numerators of convergents to coth(1)
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2009: (Start)
Equals eigensequence of an infinite lower triangular matrix with (1, 3, 5,...)
in the main diagonal, (1, 1, 1,...) in the sum diagonal, and the rest zeros. (End)
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FORMULA
| E.g.f.: cosh((1-2*x)^(1/2)-1)/(1-2*x)^(1/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 30 2004
a(n) = round( (exp(1)+exp(-1))*(BesselK(n-1/2,1)+(2*n+1)*BesselK(n+1/2,1))/sqrt(2*Pi) ) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 02 2010]
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MATHEMATICA
| a[ n_ ] := a[ n ] =a[ n-2 ]+(-1+2 n) a[ n-1 ]; a[ 0 ] := 1; a[ 1 ] := 1.
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CROSSREFS
| Cf. A001040, A001053, A036244, A036244.
Sequence in context: A163861 A006153 A183387 * A166901 A060072 A157503
Adjacent sequences: A025161 A025162 A025163 * A025165 A025166 A025167
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KEYWORD
| nonn
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AUTHOR
| w.meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), May 15 2001
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 30 2004
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