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I'm new to series and sequences. I need to understand how to write this series as an equation:

$$2^0\cdot 4+2^1\cdot 3+2^2\cdot 2+2^3\cdot 1$$

I would like this to be represented without sigma or pi notation, if possible.

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    For starters, what's the $n$th term of your sum? – 2017-01-16
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    What do you mean by write it as an equation? For instance, you could just calculate the value and write your expression equal to that value. – 2017-01-16
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    The pattern above would be for n = 4, and evaluates to 26. I want to be able to evaluate the pattern for any number of terms, like n = 8, which would be $ 2^0*8 + 2^1*7 + 2^2*6 $ ... which equals 502. – 2017-01-16
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    @DanielWilliams, it looks like you want the numbers in https://oeis.org/A000295 – 2017-01-16
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    I think it's $a_n =\sum_{i=0}^{n-1} 2^{i} (n-i)$. – 2017-01-16
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    You can prove by induction that $$2^0n+2^1(n-1)+2^2(n-2)+\cdots+2^n\cdot1=2^{n+1}-n-2$$ – 2017-01-16

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