A295451 a(n) = (14*n)!*n!/((7*n)!*(5*n)!*(3*n)!).

1, 24024, 2677114440, 347714586888240, 48026128282174802760, 6858171535488233066949024, 1000085563511096962480102423440, 147950885386878187684691046887599320, 22118704841920591519508406949192397599560, 3333326541499644169355299034603982863427892800

Offset

0,2

Links

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

Formula

G.f.: hypergeom([1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], [1/5, 1/3, 2/5, 3/5, 2/3, 4/5], 13492928512/84375*x).

a(n) = binomial(14*n,7*n)*binomial(7*n,2*n)/binomial(3*n,n) = binomial(14*n,7*n)*binomial(8*n,3*n)/binomial(8*n,n). - Chai Wah Wu, Feb 15 2026

a(n) ~ 2^(14*n) * 7^(7*n) / (3^(3*n+1/2) * 5^(5*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 23 2026

Mathematica

a[n_] := (14*n)!*n!/((7*n)!*(5*n)!*(3*n)!); Array[a, 10, 0] (* Amiram Eldar, Feb 23 2026 *)

Prog

(Python)
from math import comb
def A295451(n): return comb(14*n, 7*n)*comb(7*n, 2*n)//comb(3*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A249625 A263036 A259733 * A084691 A084692 A249843

Adjacent sequences: A295448 A295449 A295450 * A295452 A295453 A295454

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 27 2017

Status

approved