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What are the next two numbers in the following sequence:

0, 1, 4, 18, __, __.

Please explain your logic.

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closed as too broad by MikeQ, NL628, athin, Peregrine Rook, ffao May 12 '18 at 5:24

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ There are 6 pages of results on the OEIS for this sequence, including f(n) = n*n!, f(n) = n^2*fibonacci(n), f(n) = lcm(n^2, n!), and the recursive definition a(n) = 4*a(n-1) + 2*a(n-2), a(0) = 0, a(1) = 1. This is too broad. $\endgroup$ – Eric Tressler May 12 '18 at 0:07
  • $\begingroup$ Yes, and next time you come up with a similar number puzzle, please tell us if it is polynomial or not. I could find a quartic, quintic, sextic, septic, etc. polynomial that satisfies the above conditions. $\endgroup$ – NL628 May 12 '18 at 0:47
  • $\begingroup$ Agreed, @Eric Tressler and NL628. I could have applied no-computers tag, though. $\endgroup$ – Mea Culpa Nay May 12 '18 at 1:08
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I think the next two numbers are:

96 and 600

I think the pattern is:

Starting with $n=0$, the $n$th term is $n*n!$. The factorial term suggests an interpretation of the title: the exclamation mark is also a mark of surprise.
$0*0! = 0*1 = 0$
$1*1! = 1*1 = 1$
$2*2! = 2*2 = 4$
$3*3! = 3*6 = 18$
$4*4! = 4*24 = 96$
$5*5! = 5*120 = 600$
EDIT: If you don't like zero-indexed sequences, this could also start with $n=1$ and with $n$th term being $(n-1)*(n-1)!=n!-(n-1)!$. In this way, it's clear that these are the differences between successive factorials $1,1,2,6,24,120,720,...$

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  • $\begingroup$ That is correct. Too quick. Another interpretation of the terms of the sequence is n! - (n-1)!. $\endgroup$ – Mea Culpa Nay May 12 '18 at 0:15
  • $\begingroup$ I was just updating my answer to add another interpretation, actually. I think it's the one you mention, but the last part of your comment is cut off for me. EDIT: Ah, there's the rest of the comment now. I think we're playing the comment equivalent of Phone Tag at this point $\endgroup$ – ManyPinkHats May 12 '18 at 0:18

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