A295441 a(n) = (9*n)!*n!/((5*n)!*(3*n)!*(2*n)!).

1, 252, 204204, 191222460, 190004674860, 195022529167752, 204320742803699340, 217111359982448115765, 233102038867603938770220, 252255185100017685406870560, 274687728872310943504451521704, 300625891932698784845526074953032, 330384570746416514397560106035996940

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

G.f.: hypergeom([1/9, 2/9, 4/9, 5/9, 7/9, 8/9], [1/5, 2/5, 1/2, 3/5, 4/5], 14348907/12500*x).

a(n) ~ 3^(15*n + 1/2) / (2^(2*n+1) * 5^(5*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

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

Mathematica

f[n_] := (9n)! n!/((5n)! (3n)! (2n)!); Array[f, 13, 0] (* Robert G. Wilson v, Nov 23 2017 *)
(* Alternative: *)
CoefficientList[ Series[ HypergeometricPFQ[{1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, {1/5, 2/5, 1/2, 3/5, 4/5}, 14348907/12500 x], {x, 0, 12}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Prog

(Python)
from math import comb
def A295441(n): return comb(9*n, 4*n)*comb(4*n, n)//comb(2*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A179714 A109929 A351484 * A362170 A203062 A259452

Adjacent sequences: A295438 A295439 A295440 * A295442 A295443 A295444

Keyword

nonn,changed

Author

Gheorghe Coserea, Nov 23 2017

Status

approved