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URL: https://oeis.org/A295477

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A295477
a(n) = (24*n)!*n!/((12*n)!*(8*n)!*(5*n)!).
3
1, 267711444, 527048385075849780, 1217325447549161369383451760, 2994861478939539397101967737771147060, 7622711741038504461830231565042108084502603944, 19819090822775008829253654773280241192988848189242236400, 52286737777519489251960880501419064028764839670925596855165438440
OFFSET
0,2
FORMULA
G.f.: hypergeom([1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24], [1/5, 1/4, 2/5, 1/2, 3/5, 3/4, 4/5], 8916100448256/3125*x).
a(n) = binomial(24*n,12*n)*binomial(12*n,4*n)/binomial(5*n,n) = binomial(24*n,12*n)*binomial(13*n,5*n)/binomial(13*n,n). - Chai Wah Wu, Feb 16 2026
a(n) ~ 2^(24*n-3/2) * 3^(12*n) / (5^(5*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026
MATHEMATICA
a[n_] := (24*n)!*n!/((12*n)!*(8*n)!*(5*n)!); Array[a, 8, 0] (* Amiram Eldar, Feb 21 2026 *)
PROG
(Python)
from math import comb
def A295477(n): return comb(24*n, 12*n)*comb(12*n, 4*n)//comb(5*n, n) # Chai Wah Wu, Feb 16 2026
CROSSREFS
Cf. A295431.
Sequence in context: A332314 A125576 A233501 * A358484 A011578 A223605
KEYWORD
nonn,easy
AUTHOR
Gheorghe Coserea, Nov 28 2017
STATUS
approved