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For questions about sequences of integers. References are often made to the online resource oeis.org.

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A finite alternating sum

I have obtained a formula for the generating function of your sequence. Let $S_n$ be defined as in the quesion. We extend the definition to $n = 0$ by demanding $0^0 = 0$, hence $S_0 = 0$. Consider …
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1 vote

The growth of a sequence related to Liouville numbers

Not sure whether I understand correctly, but can you just take: $$v_n = \sqrt{n!}$$ (or the integer part of it)? You will then have $v_{n+1}/v_{n}=O(\sqrt{n})$, which is still $O(n)$. EDIT: Now tha …
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