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

0,2

Links

Table of n, a(n) for n=0..9.

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

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 *)

Crossrefs

Cf. A295431.

Sequence in context: A342580 A165479 A140931 * A045157 A378955 A206517

Adjacent sequences: A295437 A295438 A295439 * A295441 A295442 A295443

Keyword

nonn,changed

Author

Gheorghe Coserea, Nov 23 2017

Status

approved