A078820 a(n) = 20*C(2n,n)*(2n+1)/(n+4).

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

Links

Table of n, a(n) for n=0..24.

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

Cf. A001622, A001700, A001791, A002457, A007946, A078817, A078819.

Sequence in context: A099653 A270126 A276139 * A291395 A179417 A181305

Adjacent sequences: A078817 A078818 A078819 * A078821 A078822 A078823

Keyword

nonn,easy

Author

Henry Bottomley, Dec 07 2002

Status

approved