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A053984
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a(n)=(2*n-1)*a(n-1)-a(n-2), a(0)=0, a(1)=1.
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6
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0, 1, 3, 14, 95, 841, 9156, 118187, 1763649, 29863846, 565649425, 11848774079, 271956154392, 6787055085721, 182978531160075, 5299590348556454, 164104322274089999, 5410143044696413513, 189190902242100382956
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Numerators of successive convergents to tan(1) using continued fraction 1/(1-1/(3-1/(5-1/(7-1/(9-1/(11-1/(13-1/15-...))))))).
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 20 2009: (Start)
Equals eigensequence of an infinite lower triangular matrix with
(1, 3, 5, 7,...) as the main diagonal and (0, -1, -1, -1,...) as the subdiagonal. (End)
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FORMULA
| E.g.f.: sin(1-sqrt(1-2*x))/sqrt(1-2*x). Cf. A036244. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 10 2006
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EXAMPLE
| a(10)=565649425 because 1/(1-1/(3-1/(5-1/(7-1/(9-1/(11-1/(13-1/(15-1/(17-1/19)))))))))=565649425/363199319
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CROSSREFS
| A053984(n)=(-1)^n*A053983(-1-n). A053983(n)=-(-1)^n*A053984(-1-n).
Cf. A053983.
Sequence in context: A091906 A094369 A005772 * A113181 A136461 A007470
Adjacent sequences: A053981 A053982 A053983 * A053985 A053986 A053987
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KEYWORD
| easy,frac,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 02 2000
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EXTENSIONS
| Additional comments from Michael Somos, Aug 23, 2000
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 10 2006
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