|
| |
|
|
A000816
|
|
E.g.f.: Sum_{n >= 0} a(n) * x^(2*n) / (2*n)! = sin(x)^2 / cos(2*x).
|
|
6
| |
|
|
0, 2, 40, 1952, 177280, 25866752, 5535262720, 1633165156352, 635421069967360, 315212388819402752, 194181169538675507200, 145435130631317935357952, 130145345400688287667978240, 137139396592145493713802493952
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
LINKS
| R. J. Mathar, Table of n, a(n) for n = 1..200
|
|
|
FORMULA
| 1/2 * A002436(n), n>0. - R. Stephan, Mar 09 2004
a(n) = 2^(2*n - 1) * A000364(n) except n=0.
E.g.f.: sin(x)^2/cos(2x)=1/Q(0)-1/2; Q(k)=1+1/(1-2*(x^2)/(2*(x^2)-(k+1)*(2k+1)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 18 2011
|
|
|
MATHEMATICA
| Union[ Range[0, 26]! CoefficientList[ Series[ Sin[x]^2/Cos[ 2x], {x, 0, 26}], x]] (* Robert G. Wilson v, Apr 16 2011 *)
|
|
|
PROG
| (PARI) {a(n) = local(m); if( n<0, 0, m = 2*n; m! * polcoeff( 1 / (2 - 1 / cos(x + x * O(x^m))^2) - 1, m))} /* Michael Somos Apr 16 2011 */
|
|
|
CROSSREFS
| Cf. A000364, A000819, A000822, A000828, A003707, A009125, A009569.
Sequence in context: A198248 A163826 * A000819 A060079 A052502 A104134
Adjacent sequences: A000813 A000814 A000815 * A000817 A000818 A000819
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
