A295469 a(n) = (20*n)!*(3*n)!/((12*n)!*(10*n)!*n!).

1, 8398, 194588550, 5100249334348, 141026130105441350, 4018577033905015730148, 116743212747975158088926364, 3437433902477818949422435085400, 102221680117258170626629637553328710, 3063070065565412402561157982751304224500, 92339640658637142866394391974518333925957300

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

G.f.: hypergeom([1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20], [1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], 625000000/19683*x).

D-finite with recurrence 27*n*(12*n-11)*(12*n-1)*(6*n-1)*(12*n-5)*(2*n-1)*(12*n-7)*(6*n-5)*a(n) - 50*(20*n-11)*(20*n-9)*(20*n-7)*(20*n-3)*(20*n-1)*(20*n-19)*(20*n-17)*(20*n-13)*a(n-1) = 0. - R. J. Mathar, Jul 27 2022

a(n) = binomial(20*n,8*n)*binomial(3*n,n)/binomial(10*n,2*n) = binomial(20*n,8*n)*binomial(11*n,n)/binomial(11*n,3*n). - Chai Wah Wu, Feb 16 2026

a(n) ~ 2^(6*n-1) * 5^(10*n) / (3^(9*n) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Maple

A295469 := proc(n)
    (20*n)!*(3*n)!/((12*n)!*(10*n)!*n!) ;
end proc:
seq(A295469(n), n=0..43) ; # R. J. Mathar, Jul 27 2022

Mathematica

a[n_] := (20*n)!*(3*n)!/((12*n)!*(10*n)!*n!); Array[a, 11, 0] (* Amiram Eldar, Feb 21 2026 *)

Prog

(Python)
from math import comb
def A295469(n): return comb(20*n, 8*n)*comb(3*n, n)//comb(10*n, 2*n) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A253836 A253843 A253930 * A232300 A214117 A237137

Adjacent sequences: A295466 A295467 A295468 * A295470 A295471 A295472

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved