A295437 a(n) = (18*n)!*n!/((9*n)!*(6*n)!*(4*n)!).

1, 1021020, 6016814703900, 41477110789150966020, 304331361887290342345862940, 2309513382640863232775760738593520, 17900786683992090777583802478540374204100, 140773522690118901080808611014971776285838687000

Offset

0,2

Comments

Conjectures: for n >= 0, both a(n/2) = (9*n)!*(n/2)! / ((9*n/2)!*(3*n)!*(2*n)!) and a(n/3) = (6*n)!*(n/3)! / ((3*n)!*(2*n)!*(4*n/3)!) are integers, where fractional factorials are defined using the Gamma function; for example (n/2)! := Gamma(n/2 + 1). - Peter Bala, Jun 13 2026

Links

Table of n, a(n) for n=0..7.

Formula

G.f.: hypergeom([1/18, 5/18, 7/18, 11/18, 13/18, 17/18], [1/4, 1/3, 1/2, 2/3, 3/4], 8503056*x).

a(n) ~ 2^(4*n - 3/2) * 3^(12*n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2025

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

Mathematica

Array[(18 #)!*#!/((9 #)!*(6 #)!*(4 #)!) &, 8, 0] (* Michael De Vlieger, Nov 23 2017 *)
(* Alternative: *)
CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 11/18, 13/18, 17/18}, {1/4, 1/3, 1/2, 2/3, 3/4}, 8503056 x], {x, 0, 8}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Prog

(Python)
from math import comb
def A295437(n): return comb(18*n, 9*n)*comb(9*n, 3*n)//comb(4*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A232144 A293127 A190381 * A254265 A254258 A254304

Adjacent sequences: A295434 A295435 A295436 * A295438 A295439 A295440

Keyword

nonn,easy,changed

Author

Gheorghe Coserea, Nov 23 2017

Status

approved