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A078818
a(n) = 30*binomial(2n,n)/(n+3).
4
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
0,1
LINKS
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)
EXAMPLE
a(5) = 30*binomial(10,5)/8 = 945.
MATHEMATICA
Table[(30 Binomial[2 n, n] / (n + 3)), {n, 0, 30}] (* Vincenzo Librandi, Aug 11 2018 *)
PROG
(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
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Dec 07 2002
STATUS
approved