A295474 a(n) = (20*n)!*(7*n)!*(2*n)!/((14*n)!*(10*n)!*(4*n)!*n!).

1, 3230, 28539654, 285775341740, 3020260664350790, 32901338385286966980, 365436597301046276738460, 4114133256443603065995388440, 46780615678270404496871840084550, 536005188259178667341474315575006676, 6178692020351504220300189963052978836404, 71573683420303750522221857739718191020815080

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

G.f.: hypergeom([1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20], [1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], 10000000000/823543*x).

a(n) = binomial(20*n,6*n)*binomial(6*n,2*n)*binomial(2*n,n)/(binomial(10*n,3*n)*binomial(3*n,n)). - Chai Wah Wu, Feb 16 2026

a(n) ~ 2^(10*n-1) * 5^(10*n) / (7^(7*n) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Mathematica

a[n_] := (20*n)!*(7*n)!*(2*n)!/((14*n)!*(10*n)!*(4*n)!*n!); Array[a, 12, 0] (* Amiram Eldar, Feb 21 2026 *)

Prog

(Python)
from math import comb
def A295474(n): return comb(20*n, 6*n)*comb(6*n, 2*n)*comb(2*n, n)//(comb(10*n, 3*n)*comb(3*n, n)) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A020414 A202612 A376136 * A283578 A231141 A252611

Adjacent sequences: A295471 A295472 A295473 * A295475 A295476 A295477

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved