A295458 a(n) = (30*n)!*(5*n)!*(4*n)!/((15*n)!*(10*n)!*(8*n)!*(6*n)!).

1, 5545451340, 188242272043069768860, 7383354803839076831124554790900, 307213802011837003346320048243705086348060, 13202980048704429908831487095516759161045931997393840, 579138708444140353944173816622205024638976091097557185100664900

Offset

0,2

Links

Table of n, a(n) for n=0..6.

Formula

G.f.: hypergeom([1/30, 7/30, 11/30, 13/30, 17/30, 19/30, 23/30, 29/30], [1/8, 1/3, 3/8, 1/2, 5/8, 2/3, 7/8], 192216796875/4*x).

a(n) = binomial(30*n,15*n)*binomial(15*n,5*n)*binomial(4*n,n)/(binomial(8*n,3*n)*binomial(6*n,n)). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(9*n-1/2) * 5^(10*n) / (2^(2*n+3/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 22 2026

Mathematica

a[n_] := (30*n)!*(5*n)!*(4*n)!/((15*n)!*(10*n)!*(8*n)!*(6*n)!); Array[a, 7, 0] (* Amiram Eldar, Feb 22 2026 *)

Prog

(Python)
from math import comb
def A295458(n): return comb(30*n, 15*n)*comb(15*n, 5*n)*comb(4*n, n)//(comb(8*n, 3*n)*comb(6*n, n)) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A389009 A376255 A213254 * A058416 A343979 A210013

Adjacent sequences: A295455 A295456 A295457 * A295459 A295460 A295461

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved