Python 2, 105 bytes

a=q=[1];n=input();r=n<4;p=1 for i in range(2,n):q=a+map(sum,zip(q[1:],q))+a;r+=n in q;p*=n%i print(p+r)<1 

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Python 2, 105 104 bytes

thanks to user202729 for -1 byte

a=q=[1];n=input();r=n<4;p=1 for i in range(2,n):q=a+map(sum,zip(q[1:],q))+a;r+=n in q;p*=n%i print p+r<1 

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