A295463 a(n) = (15*n)!*(7*n)!/((14*n)!*(5*n)!*(3*n)!).

1, 105, 29029, 9166740, 3061860165, 1055101029480, 370876177263460, 132173658552875940, 47583151292491193925, 17263325497497942304176, 6301638858548635346648904, 2311724488328238270596515080, 851528189436978072303333019620, 314744785754005167603848040595140

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], 5189853515625/13492928512*x).

a(n) = binomial(15*n,n)*binomial(7*n,2*n)/binomial(3*n,n) = binomial(15*n,n)*binomial(8*n,3*n)/binomial(8*n,n). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(12*n) * 5^(10*n) / (2^(14*n+1) * 7^(7*n) * sqrt(Pi*n)). - Amiram Eldar, Feb 22 2026

Mathematica

a[n_] := (15*n)!*(7*n)!/((14*n)!*(5*n)!*(3*n)!); Array[a, 14, 0] (* Amiram Eldar, Feb 22 2026 *)

Prog

(Python)
from math import comb
def A295463(n): return comb(15*n, n)*comb(7*n, 2*n)//comb(3*n, n) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A001546 A111647 A368513 * A339847 A145621 A167779

Adjacent sequences: A295460 A295461 A295462 * A295464 A295465 A295466

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved