|
| |
|
|
A109262
|
|
A Catalan transform of the Fibonacci numbers.
|
|
5
|
|
|
|
0, 1, 2, 6, 19, 63, 215, 749, 2650, 9490, 34318, 125104, 459152, 1694914, 6287896, 23429158, 87635243, 328917615, 1238303243, 4674847097, 17692789741, 67114622451, 255120892105, 971649360211, 3707176155659, 14167390221873
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
A column of A109267.
Hankel transform is -F(2n). a(n+1) has Hankel transform F(2n+1). - Paul Barry, Nov 22 2007
|
|
|
LINKS
|
Table of n, a(n) for n=0..25.
Guo-Niu Han, Enumeration of Standard Puzzles
|
|
|
FORMULA
|
G.f.: xc(x)/(1-xc(x)-x^2c(x)^2)=(1-sqrt(1-4x))/(2(sqrt(1-4x)+x)) where c(x) is the g.f. of A000108; a(n)=sum{k=0..n, (k/(2n-k))binomial(2n-k, n-k)F(k)}.
a(n)=Sum_{k, 0<=k<=n} A106566(n,k)*A000045(k). [From Philippe DELEHAM, Oct 28 2008]
a(n)=Sum_{k, 0<=k<=n} A039599(n,k)*(-1)^(k+1)*A000045(k). [From Philippe DELEHAM, Oct 28 2008]
Conjecture: n*a(n) +(-7*n+4)*a(n-1) +(7*n-2)*a(n-2) +(19*n-60)*a(n-3) +2*(2*n-7)*a(n-4)=0. - R. J. Mathar, Nov 26 2012
|
|
|
CROSSREFS
|
Cf. A081696.
Sequence in context: A120900 A059712 A059713 * A006724 A057409 A141771
Adjacent sequences: A109259 A109260 A109261 * A109263 A109264 A109265
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Paul Barry, Jun 24 2005
|
|
|
STATUS
|
approved
|
| |
|
|
