|
| |
|
|
A104537
|
|
Expansion of (1+x)/(1+2*x+4x^2).
|
|
2
| |
|
|
1, -1, -2, 8, -8, -16, 64, -64, -128, 512, -512, -1024, 4096, -4096, -8192, 32768, -32768, -65536, 262144, -262144, -524288, 2097152, -2097152, -4194304, 16777216, -16777216, -33554432, 134217728, -134217728, -268435456, 1073741824, -1073741824, -2147483648, 8589934592
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| a(n+1) is the Hankel transform of C(2n,n)-C(2n+2,n+1). - Paul Barry (pbarry(AT)wit.ie), Mar 14 2008
a(n+1) is the Hankel transform of C(2n,n)-2*C(n)=((n-1)/(n+1))*C(2n,n), where C(n)=A000108(n). - Paul Barry (pbarry(AT)wit.ie), Mar 14 2008
|
|
|
FORMULA
| a(n) = -2*a(n-1) - 4*a(n-2).
a(n) = 2^n*cos(2*pi*n/3).
a(n) = Sum_{k, 0<=k<=n}A098158(n,k)*(-1)^k*3^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]
a(n) = (1/2)*{[ -1+I*sqrt(3)]^n+[ -1-I*sqrt(3)]^n}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
a(n) = 3^n/2^n*product(i=1,n,1/3-tan((i-1/2)*Pi/(2*n))^2) - [Gerry Martens, May 26 2011]
|
|
|
CROSSREFS
| Sequence in context: A079458 A138230 A128018 * A019240 A093907 A116471
Adjacent sequences: A104534 A104535 A104536 * A104538 A104539 A104540
|
|
|
KEYWORD
| easy,sign
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 13 2005
|
| |
|
|
