A295442 a(n) = (18*n)!*(5*n)!*(3*n)!/((10*n)!*(9*n)!*(6*n)!*n!).

1, 4862, 65132550, 987291797996, 15789207515217990, 260227401685879140612, 4372592850984736084611996, 74468439316740019538310543000, 1280895791499708481382281179968070, 22200471460266930185258813786107130900, 387105235604016899402464538876438270501300

Offset

0,2

Comments

For n >= 0, a(n/2) = (9*n)!*(5*n/2)!*(3*n/2)!/((5*n)!*(9*n/2)!*(3*n)!*(n/2)!) is an integer, where fractional factorials are defined using the Gamma function. For example, (5*n/2)! := Gamma(5*n/2 + 1). - Peter Bala, Jun 13 2026

Links

Table of n, a(n) for n=0..10.

Formula

G.f.: hypergeom([1/18, 5/18, 7/18, 11/18, 13/18, 17/18], [1/10, 3/10, 1/2, 7/10, 9/10], 57395628/3125*x).

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

a(n) = binomial(18*n,8*n)*binomial(3*n,n)*binomial(2*n,n)/(binomial(9*n,n)*binomial(6*n,n)). - Chai Wah Wu, Feb 15 2026

Mathematica

f[n_] := (18n)! (5n)! (3n)!/((10n)! (9n)! (6n)! n!); Array[f, 11, 0] (* Robert G. Wilson v, Nov 23 2017 *)
(* Alternative: *)
CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 11/18, 13/18, 17/18}, {1/10, 3/10, 1/2, 7/10, 9/10}, 57395628/3125 x], {x, 0, 10}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Prog

(Python)
from math import comb
def A295442(n): return comb(18*n, 8*n)*comb(3*n, n)*comb(2*n, n)//(comb(9*n, n)*comb(6*n, n)) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A258496 A258397 A215549 * A227599 A321978 A147697

Adjacent sequences: A295439 A295440 A295441 * A295443 A295444 A295445

Keyword

nonn,easy,changed

Author

Gheorghe Coserea, Nov 23 2017

Status

approved