A295457 a(n) = (15*n)!*(4*n)!/((8*n)!*(6*n)!*(5*n)!).

1, 9009, 294076965, 11030686038900, 438321132020096325, 17979827428611358281384, 752553618012140145142587492, 31940836366106723747518143741060, 1369603448067362789909481679723040325, 59188587562897050669538613520932321886000, 2573718443318168289438405066554782451258688840

Offset

0,2

Links

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

Formula

G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/8, 1/6, 3/8, 1/2, 5/8, 5/6, 7/8], 192216796875/4194304*x).

a(n) = binomial(15*n,7*n)*binomial(7*n,n)/binomial(5*n,n) = binomial(15*n,7*n)*binomial(11*n,5*n)/binomial(11*n,4*n). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(9*n) * 5^(10*n) / (2^(22*n+3/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 22 2026

Mathematica

a[n_] := (15*n)!*(4*n)!/((8*n)!*(6*n)!*(5*n)!); Array[a, 11, 0] (* Amiram Eldar, Feb 22 2026 *)

Prog

(Python)
from math import comb
def A295457(n): return comb(15*n, 7*n)*comb(7*n, n)//comb(5*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A106770 A326319 A102484 * A359845 A252456 A196994

Adjacent sequences: A295454 A295455 A295456 * A295458 A295459 A295460

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved