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I have a centered random variables $Y_1,Y_2$ which first 10 moments are given respectively by

$$ 0, 1, 0, 6, 0, 90, 0, 2520, 0, 113400 $$

$$0, 1, 0, 32/3, 0, 36847/100, 0, 436879364/15435, 0, 71230188570971/17781120$$

May be someone is able to conjecture what is the law of $Y_1$ and/or $Y_2$. I.e. may be some "well-known" law has the same moments.

The above values are limit cases of parametrised family of laws in (www.mimuw.edu.pl/~pmilos/moments.pdf) which I am in fact interested about. In principle, I could calculate higher momements using some recursive formula but its gets too complicated (even for mathematica).

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    $\begingroup$ How you got the moments of $Y_2$? Because in OEIS is no sequence with the given numerators: oeis.org/search?q=1%2C32%2C36847. This reduces the chance that $Y_2$ is "well-known". Maybe some more information is helpful. $\endgroup$
    – André Schlichting
    Commented Jul 29, 2011 at 13:48
  • $\begingroup$ Oh, I did not know about this website. Thanks. And answering to your question: it is limit case (as p->+\infty) of a sequence which is in pdf file mentioned above) $\endgroup$
    – Piotr Miłoś
    Commented Jul 29, 2011 at 14:21

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The first sequence can be obtained with the pdf $f(x)=e^{-\sqrt2|x|}/\sqrt2\;$, the moments of order $2n$ being $(2n)!/2^n$.

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  • $\begingroup$ I have just notice the same. But you probably mean f(x) = c e^{-\sqrt{t}|x|} i.e. symmetrized exponential distribution. $\endgroup$
    – Piotr Miłoś
    Commented Jul 29, 2011 at 13:36
  • $\begingroup$ Piotr, you could read again Andrew's solution, you will see it is correct. (And while we are at it, what about thanking the guy?) $\endgroup$
    – Did
    Commented Aug 8, 2011 at 13:52

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