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A024283
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Expansion of tan(x)^2/2.
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3
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0, 1, 8, 136, 3968, 176896, 11184128, 951878656, 104932671488, 14544442556416, 2475749026562048, 507711943253426176, 123460740095103991808, 35125800801971979943936, 11559592093904798920736768
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of cyclically reverse alternating permutations of length 2n+1, cf. A024255. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 20 2007
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 259, T(n,2).
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FORMULA
| G.f.: (1/2)*(tan(z))^2 = (z^2/(1-z^2)/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
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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
| Tan[ x ]^2/2 (* Even Part *)
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CROSSREFS
| A009764.
Cf. A009764, A000182. A diagonal of A059419.
Sequence in context: A132869 A036915 A049211 * A134053 A136472 A145404
Adjacent sequences: A024280 A024281 A024282 * A024284 A024285 A024286
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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 03/97.
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