A295447 a(n) = (14*n)!*(3*n)!/((9*n)!*(7*n)!*n!).

1, 286, 196650, 152743696, 125117624170, 105603640815036, 90864922211333424, 79239192984544856640, 69787746378451035806058, 61932198387397883017437250, 55292497255461005096459802900, 49606246898694412506503464226400, 44685036796879893398022369751697200

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

G.f.: hypergeom([1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], [1/9, 2/9, 4/9, 5/9, 7/9, 8/9], 13492928512/14348907*x).

a(n) = binomial(14*n,5*n)*binomial(3*n,n)/binomial(7*n,2*n) = binomial(14*n,5*n)*binomial(8*n,n)/binomial(8*n,3*n). - Chai Wah Wu, Feb 15 2026

a(n) ~ 2^(14*n) * 7^(7*n) / (3^(15*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 23 2026

Mathematica

a[n_] := (14*n)!*(3*n)!/((9*n)!*(7*n)!*n!); Array[a, 13, 0] (* Amiram Eldar, Feb 23 2026 *)

Prog

(Python)
from math import comb
def A295447(n): return comb(14*n, 5*n)*comb(3*n, n)//comb(7*n, 2*n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A306144 A130433 A140926 * A203049 A306788 A259402

Adjacent sequences: A295444 A295445 A295446 * A295448 A295449 A295450

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 27 2017

Status

approved