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Search: id:A025164
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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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+0
2
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| 1, 4, 21, 151, 1380, 15331, 200683, 3025576, 51635475, 984099601, 20717727096, 477491822809, 11958013297321, 323343850850476, 9388929687961125, 291380164177645351, 9624934347550257708, 337164082328436665131
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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
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E.g.f.: cosh((1-2*x)^(1/2)-1)/(1-2*x)^(1/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 30 2004
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MATHEMATICA
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a[ n_ ] := a[ n ] =a[ n-2 ]+(-1+2 n) a[ n-1 ]; a[ 0 ] := 1; a[ 1 ] := 1.
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CROSSREFS
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Cf. A001040, A001053, A036244, A036244.
Sequence in context: A006879 A163861 A006153 this_sequence A060072 A157503 A144010
Adjacent sequences: A025161 A025162 A025163 this_sequence A025165 A025166 A025167
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KEYWORD
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nonn
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AUTHOR
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w.meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
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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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