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a(n) = Product_{k=1..n} (64 - 8/k).
7

%I #19 Jan 03 2021 13:00:26

%S 1,56,3360,206080,12776960,797282304,49963024384,3140532961280,

%T 197853576560640,12486759054049280,789163172215914496,

%U 49932506169297862656,3162392057388864634880,200447004252955727626240,12714067126901763295150080,806919460320698577132191744

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

%C 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).

%H Harvey P. Dale, <a href="/A216704/b216704.txt">Table of n, a(n) for n = 0..553</a>

%p seq(product(64-8/k, k=1.. n), n=0..20);

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

%t Table[Product[64-8/k,{k,n}],{n,0,20}] (* _Harvey P. Dale_, Sep 23 2017 *)

%Y Cf. A004988, A049382, A004994, A216702, A216703.

%K nonn

%O 0,2

%A _Michel Lagneau_, Sep 16 2012