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I know it's a simple question, but I keep getting different general formulas for the coefficients when I am trying to use the multinomial theorem for the following: $$ \left(\sum_{k=0}^{M}\frac{(-x^2)^k}{4^kn^{k/2}k!(1+k)!}\right)^n $$ Please help me to calculate it.

Thank you.

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    Unforntunately it's not $(1-k)!$ ([W|A](http://tinyurl.com/bto7sfc)), but where it come from? [Bessel functions](http://en.wikipedia.org/wiki/Bessel_function)? At least [Wolfram](http://tinyurl.com/cu5jzwa) says that...2012-06-25
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    It comes from the calculation of integral with Bessel J_1 function. I;ve changed the sum to the finite, maybe it will be easier...2012-06-25
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    [Wolfram](http://tinyurl.com/cmlkud8) can give you some examples. Can one of your formulas reproduce that?2012-06-25
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    Thank you. Well, I've got formulas for n=2 and n=3 right. But I need to get a general formula for the coefficients and I am getting it wrong...2012-06-25
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    Why not posting your solutions?2012-06-26

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