A295439 a(n) = (9*n)!*(4*n)!/((8*n)!*(3*n)!*(2*n)!).

1, 18, 714, 32175, 1531530, 75167268, 3762157035, 190878381495, 9781950631050, 505159120481400, 26246321470970964, 1370400311694822954, 71844872838316074315, 3779480916094795749180, 199405648908172208299875, 10547211550872819183622800, 559103542410000371874708618

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

G.f.: hypergeom([1/9, 2/9, 4/9, 5/9, 7/9, 8/9], [1/8, 3/8, 1/2, 5/8, 7/8], 14348907/262144*x).

a(n) ~ 3^(15*n + 1/2) / (2^(18*n + 3/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

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

Mathematica

f[n_] := (9 n)! (4 n)!/((8 n)!*(3 n)! (2 n)!); Array[f, 17, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, {1/8, 3/8, 1/2, 5/8, 7/8}, 14348907/262144 x], {x, 0, 16}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Prog

(Python)
from math import comb
def A295439(n): return comb(9*n, n)*comb(4*n, n)//comb(2*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A046674 A073421 A346216 * A159873 A259458 A180781

Adjacent sequences: A295436 A295437 A295438 * A295440 A295441 A295442

Keyword

nonn

Author

Gheorghe Coserea, Nov 23 2017

Status

approved