A295435 a(n) = (12*n)!*(3*n)!/((6*n)!*(5*n)!*(4*n)!).

1, 1386, 6374082, 33660501840, 188276393811330, 1087036407409838886, 6403774152656100209808, 38253942248288803868931624, 230861076790453965336241603458, 1404158783195280855598258861670940, 8593283348445510533260633624776561582, 52853021730805678055150543201466838900800

Offset: 0

Author

Gheorghe Coserea, Nov 23 2017

Keywords

• nonn

Crossrefs

Cf. A295431.

Programs

Mathematica

Array[(12 #)!*(3 #)!/((6 #)!*(5 #)!*(4 #)!) &, 12, 0] (* Michael De Vlieger, Nov 23 2017 *)
CoefficientList[ Series[ HypergeometricPFQ[{1/12, 1/3, 5/12, 7/12, 2/3, 11/12}, {1/5, 2/5, 1/2, 3/5, 4/5}, 20155392/3125 x], {x, 0, 11}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/12, 1/3, 5/12, 7/12, 2/3, 11/12], [1/5, 2/5, 1/2, 3/5, 4/5], 20155392/3125*x).

a(n) ~ 2^(10*n-1) * 3^(9*n + 1/2) / (5^(5*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025