A216704 a(n) = Product_{k=1..n} (64 - 8/k).

1, 56, 3360, 206080, 12776960, 797282304, 49963024384, 3140532961280, 197853576560640, 12486759054049280, 789163172215914496, 49932506169297862656, 3162392057388864634880, 200447004252955727626240, 12714067126901763295150080, 806919460320698577132191744

Offset: 0

Author

Michel Lagneau, Sep 16 2012

Keywords

• nonn

Comments

This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..553

Crossrefs

Cf. A004988, A049382, A004994, A203146, A216702, A216703.

Programs

Maple

seq(product(64-8/k, k=1.. n), n=0..20);
seq((8^n/n!)*product(8*k+7, k=0.. n-1), n=0..20);

Mathematica

Table[Product[64-8/k,{k,n}],{n,0,20}] (* Harvey P. Dale, Sep 23 2017 *)

Formula

From Amiram Eldar, Aug 17 2025: (Start)

a(n) = 64^n * Gamma(n+7/8) / (Gamma(7/8) * Gamma(n+1)).

a(n) ~ c * 64^n / n^(1/8), where c = 1/Gamma(7/8) = 1/A203146 = 0.917723... . (End)