A295466 - OEIS

A295466

a(n) = (15*n)!*(6*n)!*n!/((12*n)!*(5*n)!*(3*n)!*(2*n)!).

1, 1365, 6531525, 36155455908, 212422672667205, 1289347174337943240, 7988578284829726217700, 50202452144162092092126900, 318773474802860214828983563845, 2040213003374489097738224937634800, 13139471029644309699515037254016803400, 85049362365373576290876509860293890825640

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OFFSET

0,2

LINKS

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

FORMULA

G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/12, 1/4, 5/12, 1/2, 7/12, 3/4, 11/12], 7119140625/1048576*x).

a(n) = binomial(15*n,3*n)*binomial(6*n,n)/binomial(2*n,n). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(6*n) * 5^(10*n) / (2^(20*n+3/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

MATHEMATICA

a[n_] := (15*n)!*(6*n)!*n!/((12*n)!*(5*n)!*(3*n)!*(2*n)!); Array[a, 12, 0] (* Amiram Eldar, Feb 21 2026 *)

PROG

(Python)

from math import comb

def A295466(n): return comb(15*n, 3*n)*comb(6*n, n)//comb(2*n, n) # Chai Wah Wu, Feb 16 2026

CROSSREFS

Cf. A295431.

Sequence in context: A140936 A022204 A015405 * A292780 A180089 A020409

Adjacent sequences: A295463 A295464 A295465 * A295467 A295468 A295469

KEYWORD

nonn,easy

AUTHOR

Gheorghe Coserea, Nov 28 2017

STATUS

approved