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a(n) = (9*n)!*(2*n)!/((6*n)!*(4*n)!*n!).
1

%I #10 Nov 28 2017 11:50:27

%S 1,42,3978,426075,48141450,5605430292,665398273995,80056334499603,

%T 9727795137150090,1191070745968697880,146715992699777718228,

%U 18161051595569811828018,2257160798030399890529355,281490217405724159448825420,35206768357722972409203943875,4414468429202421653755921429200

%N a(n) = (9*n)!*(2*n)!/((6*n)!*(4*n)!*n!).

%F G.f.: hypergeom([1/9, 2/9, 4/9, 5/9, 7/9, 8/9], [1/6, 1/4, 1/2, 3/4, 5/6], 531441/4096*x).

%t f[n_] := (9n)! (2n)!/((6n)!*(4n)! n!); Array[f, 16, 0] (* or *)

%t CoefficientList[ Series[ HypergeometricPFQ[{1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, {1/6, 1/4, 1/2, 3/4, 5/6}, 531441/4096 x], {x, 0, 15}], x] (* _Robert G. Wilson v_, Nov 23 2017 *)

%Y Cf. A295431.

%K nonn

%O 0,2

%A _Gheorghe Coserea_, Nov 23 2017