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Combinatorics

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Moderate

Triple Sum of Multinomial Coefficients

COMBIN-CELEVC

What is the value of the sum:

$$\sum {6\choose k_1, k_2, k_3} 2^{k_1}$$

...where the summation is over all triples of nonnegative integers $(k_1,k_2,k_3)$ with $k_1+k_2+k_3=6$?

A

$64$

B

$256$

C

$512$

D

$1024$

E

$4096$