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A371598 a(n) = (Product_{i=1..n} Fibonacci(i)) mod Fibonacci(n + 1).

%I A371598 #36 Apr 24 2024 13:23:47
%S A371598 0,1,2,1,6,6,12,2,15,16,0,49,299,220,882,252,2176,166,495,5720,5251,
%T A371598 6065,28224,41650,106947,113288,256737,173841,26840,25379,444150,
%U A371598 347278,1834953,8709610,4046544,2653673,31127545,47532000,50717205,147239197,97769672,37543458
%N A371598 a(n) = (Product_{i=1..n} Fibonacci(i)) mod Fibonacci(n + 1).
%F A371598 a(n) = A003266(n) mod A000045(n+1).
%e A371598 a(1) = 0 since A000045(1) = A000045(2) = 1 and 1 mod 1 = 0.
%e A371598 a(2) = (1 * 1) mod 2 = 1.
%e A371598 a(3) = (1 * 1 * 2) mod 3 = 2.
%e A371598 a(4) = (1 * 1 * 2 * 3) mod 5 = 1.
%t A371598 a[n_] := Mod[Fibonorial[n], Fibonacci[n + 1]]; Array[a, 50] (* _Amiram Eldar_, Mar 29 2024 *)
%o A371598 (Python)
%o A371598 from sympy import fibonacci
%o A371598 def a(n):
%o A371598     a_n = 1
%o A371598     mod = fibonacci(n + 1)
%o A371598     for i in range(1, n + 1):
%o A371598         a_n = (a_n * fibonacci(i)) % mod
%o A371598     return a_n
%o A371598 (PARI) a(n) = my(f=fibonacci(n+1)); lift(prod(k=1, n, Mod(fibonacci(k), f))); \\ _Michel Marcus_, Apr 03 2024
%Y A371598 Cf. A000045, A003266, A062347, A333599.
%K A371598 nonn
%O A371598 1,3
%A A371598 _Adnan Baysal_, Mar 29 2024