A332409 a(n) = n!! mod Fibonacci(n).

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

Author

Andrew Nelson, Feb 17 2020

Keywords

• nonn
• easy

Comments

a(n) = 0 for n = 1, 2, 5, 6, 12 (a(n) < 500).

Examples

			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.
		

Crossrefs

Cf. A000045, A006882, A182213.

Programs

Mathematica

Table[Mod[n!!,Fibonacci[n]],{n,50}] (* Harvey P. Dale, Sep 08 2020 *)

PARI

a0(n) = my(f=fibonacci(n)); prod(i=0, (n-1)\2, n - 2*i) % f; \\ Michel Marcus, Mar 17 2020

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.