Closed form for a sum Please, i need help with this example, step by step.
Calculate the value of the next summation, i.e. express simple formula without the sum:
$$\sum_{n_1 + n_2 + n_3 + n_4 = 5} \frac{6^{n_2-n_4} (-7)^{n_1}}{n_1! n_2! n_3! n_4!}$$

I think the formula is

$\sum_{n1 + n2 + n3 + n4 = n} = \frac{n!* x^{n_1} * x2^{n_2} * x3^{n_3}* x4^{n_4}}{n2! n2! n3! n4!}$
I don't know how to proceed, i stuck here.
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Can i do this with expression?
$$\sum_{n_1 + n_2 + n_3 + n_4 = 5} \frac{5! *(-7)^{n_1} * 6^{n_2} * 1^{n3} * (1/6)^{n_4}}{n_1! n_2! n_3! n_4!}$$
What next? I just put value into original expression
