A295432 a(n) = (12*n)!*(3*n)!*(2*n)!/((6*n)!*(6*n)!*(4*n)!*n!).

1, 462, 579462, 825012300, 1240292449350, 1922257130698212, 3037843525927941276, 4866407206411278522456, 7873830606510488097067590, 12837724391783995395083457780, 21058175422921386792478888300212, 34712605923460405627194955063564200

Offset: 0

Author

Gheorghe Coserea, Nov 23 2017

Keywords

• nonn

Crossrefs

Cf. A295431.

Programs

Mathematica

Array[(12 #)!*(3 #)!*(2 #)!/((6 #)!*(6 #)!*(4 #)!*#!) &, 12, 0] (* Michael De Vlieger, Nov 23 2017 *)
CoefficientList[ Series[ HypergeometricPFQ[{1/12, 5/12, 7/12, 11/12}, {1/6, 1/2, 5/6}, 1728 x], {x, 0, 11}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/12, 5/12, 7/12, 11/12], [1/6, 1/2, 5/6], 1728*x).

a(n) = a(n-1)*6*(12*n - 1)*(12*n - 5)*(12*n - 7)*(12*n - 11)/(n*(2*n - 1)*(6*n - 1)*(6*n - 5)). - Neven Sajko, Jul 22 2023

a(n) ~ 2^(6*n - 1) * 3^(3*n) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2025