A295443 a(n) = (18*n)!*(4*n)!/((12*n)!*(9*n)!*n!).

1, 884, 1887900, 4549731788, 11560065522460, 30261639292482384, 80752826621895569988, 218391531192704847549000, 596486567319455105649942300, 1641564850552143323096960793200, 4544894671462411776709731603900400, 12644660098250754851503216626543200748

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

G.f.: hypergeom([1/18, 5/18, 7/18, 1/2, 11/18, 13/18, 17/18], [1/12, 1/3, 5/12, 7/12, 2/3, 11/12], 2916*x).

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

a(n) = binomial(18*n,6*n)*binomial(4*n,n)/binomial(9*n,3*n) = binomial(18*n,6*n)*binomial(10*n,n)/binomial(10*n,4*n). - Chai Wah Wu, Feb 15 2026

Mathematica

f[n_] := (18n)! (4n)!/((12n)! (9n)! n!); Array[f, 12, 0] (* Robert G. Wilson v, Nov 23 2017 *)
(* Alternative: *)
CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 1/2, 11/18, 13/18, 17/18}, {1/12, 1/3, 5/12, 7/12, 2/3, 11/12}, 2916 x], {x, 0, 11}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Prog

(Python)
from math import comb
def A295443(n): return comb(18*n, 6*n)*comb(4*n, n)//comb(9*n, 3*n)  # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A253507 A282156 A318200 * A261760 A031794 A020393

Adjacent sequences: A295440 A295441 A295442 * A295444 A295445 A295446

Keyword

nonn,changed

Author

Gheorghe Coserea, Nov 23 2017

Status

approved