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

0,2

Links

Table of n, a(n) for n=0..15.

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

a(n) = binomial(9*n,3*n)*binomial(2*n,n)/binomial(4*n,n) = binomial(9*n,3*n)*binomial(5*n,n)/binomial(5*n,2*n). - Chai Wah Wu, Feb 15 2026

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 *)

Prog

(Python)
from math import comb
def A295438(n): return comb(9*n, 3*n)*comb(2*n, n)//comb(4*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A255959 A348812 A309193 * A294974 A263057 A048538

Adjacent sequences: A295435 A295436 A295437 * A295439 A295440 A295441

Keyword

nonn

Author

Gheorghe Coserea, Nov 23 2017

Status

approved