A295478 a(n) = (24*n)!*(5*n)!*(2*n)!/((12*n)!*(10*n)!*(8*n)!*n!).

1, 2124694, 17116035801030, 156955248839610299260, 1520823957776376583242698310, 15195903357109656115403419318791444, 154846359560326628948765847970927516623900, 1599554665194478490546369090543508578392036048440

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..142

Formula

G.f.: hypergeom([1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24], [1/10, 1/4, 3/10, 1/2, 7/10, 3/4, 9/10], 34828517376/3125*x).

a(n) = binomial(24*n,12*n)*binomial(12*n,2*n)*binomial(2*n,n)/(binomial(8*n,3*n)*binomial(3*n,n)). - Chai Wah Wu, Feb 16 2026

a(n) ~ 2^(16*n-3/2) * 3^(12*n) / (5^(5*n) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Mathematica

Table[((24n)!(5n)!(2n)!)/((12n)!(10n)!(8n)!n!), {n, 0, 10}] (* Harvey P. Dale, Jun 14 2025 *)

Prog

(Python)
from math import comb
def A295478(n): return comb(24*n, 12*n)*comb(12*n, 2*n)*comb(2*n, n)//(comb(8*n, 3*n)*comb(3*n, n)) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A253058 A233979 A203786 * A043630 A252627 A323498

Adjacent sequences: A295475 A295476 A295477 * A295479 A295480 A295481

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved