|
| |
|
|
A009531
|
|
Expansion of sin(x)*(1+x).
|
|
9
| |
|
|
0, 1, 2, -1, -4, 1, 6, -1, -8, 1, 10, -1, -12, 1, 14, -1, -16, 1, 18, -1, -20, 1, 22, -1, -24, 1, 26, -1, -28, 1, 30, -1, -32, 1, 34, -1, -36, 1, 38, -1, -40, 1, 42, -1, -44, 1, 46, -1, -48, 1, 50, -1, -52, 1, 54, -1, -56, 1, 58, -1, -60, 1, 62, -1, -64, 1, 66, -1, -68, 1, 70, -1, -72, 1, 74, -1, -76, 1, 78, -1, -80
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
FORMULA
| There's an obvious formula for the n-th term!
G.f.: x(1+x)^2/(1+x^2)^2.
abs(a(n))=sum{k=0..floor((n-1)/2), (C(n-k-1, k) mod 2)(-1)^k*2^A000120(n-2k-1)} - Paul Barry (pbarry(AT)wit.ie), Jan 06 2005
a(n) =(n^(n+1) mod (n+1)) * (-1)^[(n-1)/2] =a(n-1)-a(n-2)+(-1)^n*a(n-1) =-2a(n-2)-a(n-4). - Henry Bottomley (se16(AT)btinternet.com), May 07 2005
a(n+2) is the Hankel transform of A086622(n+1). - Paul Barry (pbarry(AT)wit.ie), Nov 06 2007
E.g.f.: sin(x)*(1+x)=x*Q(0); Q(k)=1+x/(1-x/(x-2*(k+1)*(2k+3)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 18 2011
|
|
|
CROSSREFS
| Cf. A009001.
Cf. A029578.
Sequence in context: A161510 A083258 A083259 * A124625 A137374 A131516
Adjacent sequences: A009528 A009529 A009530 * A009532 A009533 A009534
|
|
|
KEYWORD
| sign,easy
|
|
|
AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
|
| |
|
|
