Another number sequence

Question

Any ideas of what comes next?

0, 0, 1, 5, 119....

Note: this sequence cannot be found in The On-Line Encyclopedia of Integer Sequences and the solution is not obtained by fitting a polynomial function to these numbers

Answer 1

They are

the factorials of the Fibonacci numbers minus 1.

Or

$$a_n = F_n! - 1$$

For example

$$1! - 1 = 0$$ $$1! - 1 = 0$$ $$2! - 1 = 1$$ $$3! - 1 = 5$$ $$5! - 1 = 119$$ $$\cdots$$

Thus, the next number is

$$8! - 1 = \boxed{40319}$$

Answer 2

I believe one should always include the fact that THE REAL ANSWER IS SIMPLE

as the solution

$f(x) = \dfrac{35}{8}x^4 - \dfrac{311}{12}x^3+\dfrac{381}{8}x^2-\dfrac{313}{12} x$

also works...