OFFSET
1,2
COMMENTS
Odd coefficients are zero.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..250
FORMULA
2*acot(cos(x)) = Pi/2 + x^2/2! + 2*x^4/4! + x^6/6! - 148*x^8/8! - 3719*x^10/10! -...
2*atan(cos(x)) = Pi/2 - x^2/2! - 2*x^4/4! - x^6/6! + 148*x^8/8! + 3719*x^10/10! +...
G.f. sin(x)/(1 - 1/2*sin(x)^2) = x + 2*x^3/3! + x^5/5! - 148*x^7/7! - ... - Peter Bala, Feb 06 2017
MAPLE
with(gfun):
series(sin(x)/(1-(1/2)*sin(x)^2), x, 35):
L := seriestolist(%):
seq(op(2*i, L)*(2*i-1)!, i = 1..floor((1/2)*nops(L)));
# Peter Bala, Feb 06 2017
MATHEMATICA
With[{nn=40}, Take[CoefficientList[Series[2ArcCot[Cos[x]], {x, 0, nn}], x] Range[0, nn]!, {3, -1, 2}]] (* Harvey P. Dale, Nov 17 2014 *) (* adapted by Vincenzo Librandi, Feb 07 2017 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Ralf Stephan, Dec 27 2004
EXTENSIONS
More terms from Harvey P. Dale, Nov 17 2014
Signs of the data entries corrected by Peter Bala, Feb 06 2017
STATUS
approved