Pip -x, 20 1414 13 bytes
L#al+Lgl+:lPE!ll=all=g Try it here! TIO doesn't support the -x flag, but you can simulate it using Takes the header:list of numbers as separate command-line arguments. Try it online!Attempt This Online!
Explanation
We generate the nth row of Pascal's triangle, where n is the length of the input list; then we output truthy if the row and the input are equal, falsey otherwise. Heavily based on my answer to Generate Pascal's triangle, which I recommend you read for a better explanation of the core algorithm.
ag is 1st cmdline arg,list evaluatedof (-xcmdline flag);args; l is empty list L Loop #ag len(ag) times: !l 1 if l is empty, 0 otherwise lPE l with that value prepended l+: Add to l itemwise and assign back to l l=al=g 1 if l equals ag, 0 otherwise