A295480 a(n) = (24*n)!*(7*n)!*(4*n)!/((14*n)!*(12*n)!*(8*n)!*n!).

1, 44574, 5512410886, 770205244644780, 113493385509758105670, 17232366122881987992336324, 2667342121225036254551827535260, 418446897672874336912068988103878680, 66297659655162356848194576725889346695750, 10584121412183743053352396456036397314784501460

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Formula

G.f.: hypergeom([1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24], [1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], 139314069504/823543*x).

a(n) = binomial(24*n,10*n)*binomial(4*n,2*n)*binomial(2*n,n)/(binomial(12*n,2*n)*binomial(8*n,n)). - Chai Wah Wu, Feb 17 2026

a(n) ~ 2^(18*n-1) * 3^(12*n) / (7^(7*n) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Mathematica

a[n_] := (24*n)!*(7*n)!*(4*n)!/((14*n)!*(12*n)!*(8*n)!*n!); Array[a, 10, 0] (* Amiram Eldar, Feb 21 2026 *)

Prog

(Python)
from math import comb
def A295480(n): return comb(24*n, 10*n)*comb(4*n, 2*n)*comb(2*n, n)//(comb(12*n, 2*n)*comb(8*n, n)) # Chai Wah Wu, Feb 17 2026

Crossrefs

Cf. A295431.

Sequence in context: A258514 A258507 A254994 * A206166 A206380 A204786

Adjacent sequences: A295477 A295478 A295479 * A295481 A295482 A295483

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved