OFFSET
0,1
FORMULA
D-finite with recurrence a(n) = a(n-1)*(4n^2+14n+6)/(n^2+4n) = A078817(3, n) = (2n+1)*A078819(n)/7 = 20*A002457(n)/(n+4).
From Amiram Eldar, Feb 16 2023: (Start)
Sum_{n>=0} 1/a(n) = 11*Pi/(90*sqrt(3)) + 1/30.
Sum_{n>=0} (-1)^n/a(n) = 17*log(phi)/(25*sqrt(5)) + 1/50, where phi is the golden ratio (A001622). (End)
EXAMPLE
a(5)=20*C(10,5)*11/9=6160.
MATHEMATICA
Table[20Binomial[2n, n] (2n+1)/(n+4), {n, 0, 30}] (* Harvey P. Dale, Nov 02 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Dec 07 2002
STATUS
approved