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 A009764 Tan(x)^2 = sum(n>=0, a(n)*x^(2*n)/(2*n)! ). 4
 0, 2, 16, 272, 7936, 353792, 22368256, 1903757312, 209865342976, 29088885112832, 4951498053124096, 1015423886506852352, 246921480190207983616, 70251601603943959887872, 23119184187809597841473536, 8713962757125169296170811392, 3729407703720529571097509625856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS 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) where 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 G.f. A(x)=-1 + 1/G(0) where G(k)= 1 - (k+1)*(k+2)*x/G(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Aug 10 2012 G.f.: 1/G(0)-1 where G(k) =  1 - 2*x*(2*k+1)^2 - x^2*(2*k+1)*(2*k+2)^2*(2*k+3)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jan 13 2013 G.f.: (1/G(0)-1)*sqrt(-x), where G(k)= 1 - sqrt(-x) - x*(k+1)^2/G(k+1); (continued fraction). - Sergei N. Gladkovskii, May 29 2013 G.f.: Q(0) -1, where Q(k) = 1 - x*(k+1)*(k+2)/( x*(k+1)*(k+2) - 1/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 14 2013 EXAMPLE (tan x)^2 = x^2 + 2/3*x^4 + 17/45*x^6 + 62/315*x^8 + ... 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 *) CROSSREFS Essentially same as A000182. Cf. A024283, A000182. Sequence in context: A012188 A217816 A000182 * A189257 A227674 A102599 Adjacent sequences:  A009761 A009762 A009763 * A009765 A009766 A009767 KEYWORD nonn,easy AUTHOR EXTENSIONS Extended and signs tested Mar 15 1997 by Olivier Gérard. More terms from Harvey P. Dale, Oct 04 2011 STATUS approved

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Last modified October 20 15:55 EDT 2019. Contains 328267 sequences. (Running on oeis4.)