OFFSET
6,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 6..500
Milan Janjic, Two Enumerative Functions.
FORMULA
a(n+1) = a(n)*(2*n+2)*(2*n+3)/((n-5)*(n+8)). - Chai Wah Wu, Jan 26 2016
From Amiram Eldar, Jan 24 2022: (Start)
Sum_{n>=6} 1/a(n) = 40*Pi/(9*sqrt(3)) - 96827/13860.
Sum_{n>=6} (-1)^n/a(n) = 29248*log(phi)/(5*sqrt(5)) - 3486955/2772, where phi is the golden ratio (A001622). (End)
MATHEMATICA
Table[Binomial[2*n + 1, n - 6], {n, 6, 25}] (* Amiram Eldar, Jan 24 2022 *)
PROG
(Python)
from __future__ import division
A030056_list, b = [], 1
for n in range(6, 501):
A030056_list.append(b)
b = b*(2*n+2)*(2*n+3)//((n-5)*(n+8)) # Chai Wah Wu, Jan 26 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved