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Finding general terms of a series

Somveer Keshav
Posted 2 months ago

I want to find general terms of this series I already used command ''FindSequenceFunction''. Help me

FindSequenceFunction[{E^-m, E^-m (2 - m), 
  FullSimplify[ (1 - 2 m + m^2/2)], FullSimplify[(-m + m^2 - m^3/6)], 
  FullSimplify[ (m^2/2 - m^3/6 + m^4/24)], 
  FullSimplify[ (-(m^3/6) + m^4/24 - m^5/120)]}, m]
POSTED BY: Somveer Keshav
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Ignoring the exponential terms, the closest I arrived is this:

Table[(-m)^(n - 1)/(n + 1)!
  (n + n^2 + (m - a[n]) m),
 {n, -1, 4}]

where a[n] should come from

FindSequenceFunction[{0, 2, 4, 6, 4, 5}, n]

if only it gave an answer. I was disappointed that this too gave no answer:

FindSequenceFunction[{2, 6, 24, 120}, n]
POSTED BY: Gianluca Gorni
POSTED BY: Michael Rogers

I will venture to guess that the middle terms of the first and second elements are not quite what was intended. This would make the task more difficult.
POSTED BY: Daniel Lichtblau
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