A295440 a(n) = (18*n)!*(4*n)!*(3*n)!/((9*n)!*(8*n)!*(6*n)!*(2*n)!).

1, 43758, 7012604550, 1288415796384780, 250622090889055155270, 50312973039218473430585508, 10304958075870392958137083227804, 2140123855549810059379592073872919000, 449006091012360080585628994760351491412550, 94939602104589721712783038933265704553286808500

Offset: 0

Author

Gheorghe Coserea, Nov 23 2017

Keywords

• nonn

Crossrefs

Cf. A295431.

Programs

Mathematica

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 *)

Formula

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).

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

a(n) ~ 3^(15*n) / (2^(6*n + 3/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025