A078818 a(n) = 30*binomial(2n,n)/(n+3).

10, 15, 36, 100, 300, 945, 3080, 10296, 35100, 121550, 426360, 1511640, 5408312, 19501125, 70794000, 258529200, 949074300, 3500409330, 12964479000, 48198087000, 179799820200, 672822343050, 2524918756464, 9500112378000, 35830670759000, 135439935469020

Offset: 0

Author

Henry Bottomley, Dec 07 2002

Keywords

• nonn
• easy

Examples

			a(5) = 30*binomial(10,5)/8 = 945.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000108, A000984, A001622, A007946, A038629, A078817, A078819.

Programs

GAP

List([0..30],n->30*Binomial(2*n,n)/(n+3)); # Muniru A Asiru, Aug 09 2018

Magma

[30*Binomial(2*n,n)/(n+3): n in [0..30]]; // Vincenzo Librandi, Aug 11 2018

Mathematica

Table[(30 Binomial[2 n, n] / (n + 3)), {n, 0, 30}] (* Vincenzo Librandi, Aug 11 2018 *)

Formula

D-finite with recurrence a(n) = a(n-1)*(4n^2+6n-4)/(n^2+3n) = A078817(n, 2) = 5*A007946(n)/(2n+1) = 30*A000984(n)/(n+3).

From Amiram Eldar, Feb 16 2023: (Start)

Sum_{n>=0} 1/a(n) = 4*Pi/(135*sqrt(3)) + 7/45.

Sum_{n>=0} (-1)^n/a(n) = 9/125 - 32*log(phi)/(375*sqrt(5)), where phi is the golden ratio (A001622). (End)