Let moment-generating function($mgf$) exists for given random variable $X$ and let $$E(X^{2r})= (2r)!/2^rr! \;\;\text{where}\;\;r=1,2,3,...$$ $$E(X^{2r-1}) = 0 \;\;\text{where}\;\;r=1,2,3, ...$$ then find $mgf$ of $X$
I would like to derive pdf of $X$ from given above two equations. Is there any hint/advice for this problem?