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A009764
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Expansion of tan(x)^2.
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3
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0, 2, 16, 272, 7936, 353792, 22368256, 1903757312, 209865342976, 29088885112832, 4951498053124096, 1015423886506852352, 246921480190207983616, 70251601603943959887872, 23119184187809597841473536, 8713962757125169296170811392, 3729407703720529571097509625856
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| (tan(z))^2 = z^2/(1-z^2)*( 1 +2*z^2/( (z^2-1)*(G(0)-2*z^2)), G(k) = (k+2)*(2*k+3)-2*z^2+2*z^2*(k+2)*(2*k+3)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Dec 15 2011
(tan(z))^2 = z^2/(G(0)+z^2), G(k) = (k+1)*(2*k+1)-2*z^2+2*z^2*(k+1)*(2*k+1)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Dec 15 2011
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EXAMPLE
| (tan x)^2 = x^2 + 2/3*x^4 + 17/45*x^6 + 62/315*x^8 + ...
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MATHEMATICA
| With[{nn=30}, Take[CoefficientList[Series[Tan[x]^2, {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* From Harvey P. Dale, Oct 04 2011 *)
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CROSSREFS
| Essentially same as A000182.
Cf. A024283, A000182.
Sequence in context: A050974 A012188 A000182 * A189257 A102599 A123744
Adjacent sequences: A009761 A009762 A009763 * A009765 A009766 A009767
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KEYWORD
| nonn,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended and signs tested Mar 15 1997 by Olivier Gerard.
More terms from Harvey P. Dale, Oct 04 2011
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