[seqfan] Re: Peculiar Integer Recurrences ... Proof?
Maximilian Hasler
maximilian.hasler at gmail.com
Mon Feb 9 03:20:06 CET 2009
On Sun, Feb 8, 2009 at 4:51 PM, Robert Israel <israel at math.ubc.ca> wrote:
> It seems to work as well if 2 is replaced by any other integer.
> If a(n,x) = (1/n) Sum_{k=1..n} x^(k^2) a(n-k), with a(0)=1,
> then the polynomial a(n,x) takes integer values on the integers.
These polynomials are the cycle index polynomials of the symmetric group S_n,
denoted Z(S_n) in A102189, upon the substitution x[2] = x^2, x[3] = x^9 etc.
Maximilian
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