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

6 votes
0 answers
382 views

A strange polynomial equality

In my answer to this question, I have obtained that the polynomial $p(x)$ of degree $2n$ with nonnegative values on $[-1,1]$ with $p(\pm1)=1$ has $\int_{-1}^1 p(x)\,dx\geq \frac{4}{(n+1)(n+2)}$, and t …
Ilya Bogdanov's user avatar
35 votes
0 answers
1k views

Is there any positive integer sequence $c_{n+1}=\frac{c_n(c_n+n+d)}n$?

In a recent answer Max Alekseyev provided two recurrences of the form mentioned in the title which stay integer for a long time. However, they eventually fail. QUESTION Is there any (added: strict …
Ilya Bogdanov's user avatar