A295440 - OEIS

%I #10 Jan 13 2025 06:01:51

%S 1,43758,7012604550,1288415796384780,250622090889055155270,

%T 50312973039218473430585508,10304958075870392958137083227804,

%U 2140123855549810059379592073872919000,449006091012360080585628994760351491412550,94939602104589721712783038933265704553286808500

%N a(n) = (18*n)!*(4*n)!*(3*n)!/((9*n)!*(8*n)!*(6*n)!*(2*n)!).

%F G.f.: hypergeom([1/18, 5/18, 7/18, 11/18, 13/18, 17/18], [1/8, 3/8, 1/2, 5/8, 7/8], 14348907/64*x).

%F D-finite with recurrence n*(8*n-5)*(8*n-3)*(8*n-1)*(2*n-1)*(8*n-7)*a(n) -54*(18*n-11)*(18*n-7)*(18*n-17)*(18*n-13)*(18*n-5)*(18*n-1)*a(n-1)=0. - _R. J. Mathar_, Jan 13 2025

%t f[n_] := (18n)! (4n)! (3n)!/((9n)! (8n)! (6n)! (2n)!); Array[f, 10, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 11/18, 13/18, 17/18}, {1/8, 3/8, 1/2, 5/8, 7/8}, 14348907/64 x], {x, 0, 9}], x] (* _Robert G. Wilson v_, Nov 23 2017 *)

%Y Cf. A295431.

%K nonn,changed

%O 0,2

%A _Gheorghe Coserea_, Nov 23 2017