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a(n) = (3/(8n-4))*C(4n,n).
0

%I #18 Mar 12 2019 09:33:57

%S 3,7,33,195,1292,9177,68310,525915,4153380,33460284,273904969,

%T 2271800037,19050406788,161242554550,1375709203260,11819200090635,

%U 102162535941492,887830494976788,7752586858050900,67986848888695660,598522586288243760,5287559893638230385

%N a(n) = (3/(8n-4))*C(4n,n).

%F G.f.: (g+2)*(g-1)/g^2 where g = 1+x*g^4 is the g.f. of A002293. - _Mark van Hoeij_, Nov 11 2011

%F a(n) ~ 2^(8*n - 5/2) / (sqrt(Pi) * n^(3/2) * 3^(3*n - 1/2)). - _Vaclav Kotesovec_, Mar 12 2019

%t Table[3/(8*n - 4)*Binomial[4*n, n], {n, 1, 20}] (* _Vaclav Kotesovec_, Mar 12 2019 *)

%o (PARI) a(n) = 3*binomial(4*n, n)/(8*n-4); \\ _Michel Marcus_, Mar 12 2019

%Y Cf. A005810.

%K nonn

%O 1,1

%A _Clark Kimberling_

%E More terms from _Vaclav Kotesovec_, Mar 12 2019