A009764 Tan(x)^2 = sum(n>=0, a(n)*x^(2*n)/(2*n)! ).

0, 2, 16, 272, 7936, 353792, 22368256, 1903757312, 209865342976, 29088885112832, 4951498053124096, 1015423886506852352, 246921480190207983616, 70251601603943959887872, 23119184187809597841473536, 8713962757125169296170811392, 3729407703720529571097509625856

Offset

0,2

Links

Table of n, a(n) for n=0..16.

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}]] (* 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

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

More terms from Harvey P. Dale, Oct 04 2011

Status

approved