A295470 a(n) = (20*n)!*(6*n)!*n!/((12*n)!*(10*n)!*(3*n)!*(2*n)!).

1, 83980, 29966636700, 12398706131799988, 5447952226877283703580, 2473617870747229982625186480, 1146602219745194113307246953503300, 539110100779634346434520330628287843000, 256130864665265316470308479790547084791062300, 122657586881362583078239819278500645564891283341200

Offset

0,2

Links

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

Formula

G.f.: hypergeom([1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20], [1/12, 1/3, 5/12, 1/2, 7/12, 2/3, 11/12], 10000000000/19683*x).

a(n) = binomial(20*n,8*n)*binomial(6*n,3*n)*binomial(3*n,n)/(binomial(10*n,2*n)*binomial(2*n,n)). - Chai Wah Wu, Feb 16 2026

a(n) ~ 2^(10*n-1) * 5^(10*n) / (3^(9*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Mathematica

a[n_] := (20*n)!*(6*n)!*n!/((12*n)!*(10*n)!*(3*n)!*(2*n)!); Array[a, 10, 0] (* Amiram Eldar, Feb 21 2026 *)

Prog

(Python)
from math import comb
def A295470(n): return comb(20*n, 8*n)*comb(6*n, 3*n)*comb(3*n, n)//(comb(10*n, 2*n)*comb(2*n, n)) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A205197 A203395 A333683 * A237492 A345606 A346280

Adjacent sequences: A295467 A295468 A295469 * A295471 A295472 A295473

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved