|
| |
|
|
A067336
|
|
a(0)=1, a(1)=2, a(n)=a(n-1)*9/2-Catalan(n-1) where Catalan(n)=C(2n,n)/(n+1)=A000108(n).
|
|
7
| |
|
|
1, 2, 8, 34, 148, 652, 2892, 12882, 57540, 257500, 1153888, 5175700, 23231864, 104335376, 468766292, 2106773874, 9470787588, 42583186476, 191494694352, 861248485884, 3873850923288, 17425765034376, 78391476387672
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Note that while a(n) is even (for n>0), it is not a multiple of 4 only when n=2^m-1, i.e. when Catalan(n) is odd.
Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse of (1/(1-x),x(1-x)) to 3^n. - Paul Barry (pbarry(AT)wit.ie), Mar 12 2005
Hankel transform is A001787(n+1). [From Paul Barry (pbarry(AT)wit.ie), Mar 15 2010]
|
|
|
FORMULA
| a(n) =A067337(2n, n)
G.f.: (1+sqrt(1-4x))/(3sqrt(1-4x)-1); - Paul Barry (pbarry(AT)wit.ie), Mar 12 2005
a(n)=Sum_[k, 0<=k<=n}A039599(n,k)*A001045(k+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 10 2007
G.f.: (1-xc(x))/(1-3xc(x)), c(x) the g.f. of A000108. [From Paul Barry (pbarry(AT)wit.ie), Mar 15 2010]
|
|
|
EXAMPLE
| a(2)=2*9/2-1=8; a(3)=8*9/2-2=34; a(4)=34*9/2-5=148; a(5)=148*9/2-14=652.
|
|
|
CROSSREFS
| Cf. A088218.
Sequence in context: A014445 A113440 A034999 * A151829 A026387 A085362
Adjacent sequences: A067333 A067334 A067335 * A067337 A067338 A067339
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jan 15 2002
|
| |
|
|
