OFFSET
0,1
LINKS
Sela Fried, On the generating function of A119574, 2024.
FORMULA
Conjectured g.f.: (-1 + 14*x - 36*x^2 + (1 - 4*x)^(3/2))/(2*x*(1 - 4*x)^(3/2)). - Harvey P. Dale, Jun 02 2024.
The conjecture is true (see links). - Sela Fried, Oct 02 2024.
a(n) ~ 4^n * sqrt(n/Pi). - Amiram Eldar, Sep 20 2025
MAPLE
[seq (binomial(2*n, n)*(n+2)^2/(n+1), n=0..25)];
MATHEMATICA
Table[Binomial[2n, n] (n+2)^2/(n+1), {n, 0, 30}] (* Harvey P. Dale, Jun 02 2024 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 31 2006
STATUS
approved