A function f is defined for all real numbers and satisfies
f(0)=1,f(1)(0)=0,f(2)(0)=0,f(3)(0)=−1,f(4)(0)=0,
and, in general, f(k)(0)=(−1)k if k is divisible by 3, and f(k)(0)=0 otherwise.
What is the Maclaurin series of f?
Clarification: In the answer choices, ! denotes the factorial function. For example, 8!=1×2×3×⋯×8.