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A078820
a(n) = 20*C(2n,n)*(2n+1)/(n+4).
3
5, 24, 100, 400, 1575, 6160, 24024, 93600, 364650, 1421200, 5542680, 21633248, 84504875, 330372000, 1292646000, 5061729600, 19835652870, 77786874000, 305254551000, 1198665468000, 4709756401350, 18516070880736, 72834194898000, 286645366072000, 1128666128908500
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 *)
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Dec 07 2002
STATUS
approved