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Denominator of a remarkable product.
2

%I #12 Feb 08 2025 09:01:13

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,5,5,5,5,1,5,5,5,1,1,5,5,1,1,1,5,1,1,1,1,5,5,5,5,5,25,25,25

%N Denominator of a remarkable product.

%C There seems to be no other denominators than 1 or 5^k.

%C The first 5^k terms appear respectively at positions {76,101,1351,4476,7601,...}

%H Olivier Gérard, <a href="/A133707/b133707.txt">Table of n, a(n) for n = 1..10001</a>

%F a(n) = denominator(Product_{i=1..n-1} (394 - 225*i + 85*i^2 - 15*i^3 + i^4)/120).

%t a[n_]:= Denominator[Product[(394-225 i+85 i^2 -15 i^3+i^4)/120,{i,n-1 }]]; Array[a,103] (* _Stefano Spezia_, Feb 08 2025 *)

%Y Sequence of numerators is in A133706.

%K nonn,frac,changed

%O 1,76

%A _Olivier Gérard_, Sep 20, 2007