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A332409
a(n) = n!! mod Fibonacci(n).
0
0, 0, 1, 2, 0, 0, 1, 6, 27, 45, 71, 0, 228, 73, 605, 861, 956, 2376, 1199, 5235, 7137, 5017, 21617, 40320, 49250, 72900, 94129, 253071, 125204, 188760, 786046, 1041600, 3306329, 2717231, 8692580, 4869072, 10661888, 33618132, 14333453, 66880275, 110783982
OFFSET
1,4
COMMENTS
a(n) = 0 for n = 1, 2, 5, 6, 12 (a(n) < 500).
FORMULA
a(n) = n!! mod Fibonacci(n).
where n!! denotes the double factorial of n (n!! = n*a(n-2) for n > 1, a(0) = a(1) = 1), and Fibonacci(n) denotes the n-th Fibonacci number.
EXAMPLE
For n = 1, a(1) = 1!! mod Fibonacci(1) = 1 mod 1 = 0.
For n = 4, a(4) = 4!! mod Fibonacci(4) = 8 mod 3 = 2.
MATHEMATICA
Table[Mod[n!!, Fibonacci[n]], {n, 50}] (* Harvey P. Dale, Sep 08 2020 *)
PROG
(PARI) a0(n) = my(f=fibonacci(n)); prod(i=0, (n-1)\2, n - 2*i) % f; \\ Michel Marcus, Mar 17 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Andrew Nelson, Feb 17 2020
STATUS
approved