A295434 a(n) = (12*n)!*(3*n)!/((8*n)!*(6*n)!*n!).

1, 99, 22287, 5663700, 1517599215, 418974963099, 117912668329092, 33631821857441592, 9687910353619450095, 2811928784155292169225, 821085376403131135219287, 240930004359452293067067600, 70981901511015157572343133700, 20983636110818804086505029904100, 6221192124050298514903984159997400

Offset: 0

Author

Gheorghe Coserea, Nov 23 2017

Keywords

• nonn

Crossrefs

Cf. A295431.

Programs

Mathematica

Array[(12 #)!*(3 #)!/((8 #)!*(6 #)!*#!) &, 15, 0] (* Michael De Vlieger, Nov 23 2017 *)
CoefficientList[ Series[ HypergeometricPFQ[{1/12, 1/3, 5/12, 7/12, 2/3, 11/12}, {1/8, 3/8, 1/2, 5/8, 7/8}, 19683/64 x], {x, 0, 14}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/12, 1/3, 5/12, 7/12, 2/3, 11/12], [1/8, 3/8, 1/2, 5/8, 7/8], 19683/64*x).

a(n) ~ 3^(9*n + 1/2) / (2^(6*n + 3/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025