A295437 a(n) = (18*n)!*n!/((9*n)!*(6*n)!*(4*n)!).

1, 1021020, 6016814703900, 41477110789150966020, 304331361887290342345862940, 2309513382640863232775760738593520, 17900786683992090777583802478540374204100, 140773522690118901080808611014971776285838687000

Offset: 0

Author

Gheorghe Coserea, Nov 23 2017

Keywords

• nonn

Crossrefs

Cf. A295431.

Programs

Mathematica

Array[(18 #)!*#!/((9 #)!*(6 #)!*(4 #)!) &, 8, 0] (* Michael De Vlieger, Nov 23 2017 *)
CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 11/18, 13/18, 17/18}, {1/4, 1/3, 1/2, 2/3, 3/4}, 8503056 x], {x, 0, 8}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/18, 5/18, 7/18, 11/18, 13/18, 17/18], [1/4, 1/3, 1/2, 2/3, 3/4], 8503056*x).

a(n) ~ 2^(4*n - 3/2) * 3^(12*n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2025