A295438 a(n) = (9*n)!*(2*n)!/((6*n)!*(4*n)!*n!).

1, 42, 3978, 426075, 48141450, 5605430292, 665398273995, 80056334499603, 9727795137150090, 1191070745968697880, 146715992699777718228, 18161051595569811828018, 2257160798030399890529355, 281490217405724159448825420, 35206768357722972409203943875, 4414468429202421653755921429200

Offset: 0

Author

Gheorghe Coserea, Nov 23 2017

Keywords

• nonn

Crossrefs

Cf. A295431.

Programs

Mathematica

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

Formula

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).

a(n) ~ 3^(12*n + 1/2) / (sqrt(Pi*n) * 2^(12*n + 3/2)). - Vaclav Kotesovec, Apr 03 2025