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%I #25 Feb 16 2023 05:07:27
%S 10,15,36,100,300,945,3080,10296,35100,121550,426360,1511640,5408312,
%T 19501125,70794000,258529200,949074300,3500409330,12964479000,
%U 48198087000,179799820200,672822343050,2524918756464,9500112378000,35830670759000,135439935469020
%N a(n) = 30*binomial(2n,n)/(n+3).
%H Muniru A Asiru, <a href="/A078818/b078818.txt">Table of n, a(n) for n = 0..300</a>
%F 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).
%F From _Amiram Eldar_, Feb 16 2023: (Start)
%F Sum_{n>=0} 1/a(n) = 4*Pi/(135*sqrt(3)) + 7/45.
%F Sum_{n>=0} (-1)^n/a(n) = 9/125 - 32*log(phi)/(375*sqrt(5)), where phi is the golden ratio (A001622). (End)
%e a(5) = 30*binomial(10,5)/8 = 945.
%t Table[(30 Binomial[2 n, n] / (n + 3)), {n, 0, 30}] (* _Vincenzo Librandi_, Aug 11 2018 *)
%o (GAP) List([0..30],n->30*Binomial(2*n,n)/(n+3)); # _Muniru A Asiru_, Aug 09 2018
%o (Magma) [30*Binomial(2*n,n)/(n+3): n in [0..30]]; // _Vincenzo Librandi_, Aug 11 2018
%Y Cf. A000108, A000984, A001622, A007946, A038629, A078817, A078819.
%K nonn,easy
%O 0,1
%A _Henry Bottomley_, Dec 07 2002
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