A295465 a(n) = (30*n)!*(5*n)!*(3*n)!/((15*n)!*(12*n)!*(10*n)!*n!).

1, 84021990, 27148761423822150, 9954973275139484047762908, 3854033460136506985790722290997830, 1538140504965911180891074089844546665130740, 625941149813307100769398285275462870937611266492700, 258199006729578473819424192171981739783714836205236867089400

Offset

0,2

Links

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

Formula

G.f.: hypergeom([1/30, 7/30, 11/30, 13/30, 17/30, 19/30, 23/30, 29/30], [1/12, 1/4, 5/12, 1/2, 7/12, 3/4, 11/12], 7119140625/16*x).

a(n) = binomial(30*n,15*n)*binomial(15*n,3*n)*binomial(3*n,n)/(binomial(10*n,5*n)*binomial(5*n,2*n)). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(6*n) * 5^(10*n) / (2^(4*n+3/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Mathematica

Table[((3 n)! (5 n)! (30 n)!)/(n! (10 n)! (12 n)! (15 n)!), {n, 0, 20}] (* Harvey P. Dale, Aug 19 2020 *)

Prog

(Python)
from math import comb
def A295465(n): return comb(30*n, 15*n)*comb(15*n, 3*n)*comb(3*n, n)//(comb(10*n, 5*n)*comb(5*n, 2*n)) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A120316 A118079 A186091 * A230794 A186922 A185806

Adjacent sequences: A295462 A295463 A295464 * A295466 A295467 A295468

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved