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%I #10 Feb 16 2023 05:07:35
%S 35,56,140,400,1225,3920,12936,43680,150150,523600,1847560,6584032,
%T 23661365,85652000,312018000,1142971200,4207562730,15557374800,
%U 57750861000,215145084000,804104751450,3014244096864,11329763650800,42691863032000,161238018415500,610258100044320
%N a(n) = 140*C(2n,n)/(n+4).
%F D-finite with recurrence a(n) = a(n-1)*(4n^2+10n-6)/(n^2+4n) = A078817(n, 3) = 7*A078820(n)/(2n+1) = 140*A000984(n)/(n+4).
%F From _Amiram Eldar_, Feb 16 2023: (Start)
%F Sum_{n>=0} 1/a(n) = Pi/(126*sqrt(3)) + 3/70.
%F Sum_{n>=0} (-1)^n/a(n) = 37/1750 - 3*log(phi)/(125*sqrt(5)), where phi is the golden ratio (A001622). (End)
%e a(5)=140*C(10,5)/9=3920
%t Table[140*Binomial[2*n, n]/(n + 4), {n, 0, 30}] (* _Amiram Eldar_, Feb 16 2023 *)
%Y Cf. A000108, A000984, A001622, A038629, A078817, A078818, A078820.
%K nonn,easy
%O 0,1
%A _Henry Bottomley_, Dec 07 2002
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