OFFSET
0,1
FORMULA
D-finite with recurrence a(n) = a(n-1)*(4n^2+10n-6)/(n^2+4n) = A078817(n, 3) = 7*A078820(n)/(2n+1) = 140*A000984(n)/(n+4).
From Amiram Eldar, Feb 16 2023: (Start)
Sum_{n>=0} 1/a(n) = Pi/(126*sqrt(3)) + 3/70.
Sum_{n>=0} (-1)^n/a(n) = 37/1750 - 3*log(phi)/(125*sqrt(5)), where phi is the golden ratio (A001622). (End)
EXAMPLE
a(5)=140*C(10,5)/9=3920
MATHEMATICA
Table[140*Binomial[2*n, n]/(n + 4), {n, 0, 30}] (* Amiram Eldar, Feb 16 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Dec 07 2002
STATUS
approved