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Motzkin Numbers

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Multiple Choice

What is the generating function for Motzkin numbers?

  1. $$1 + x + x^2 + x^3 + \cdots$$
  2. $$1 + x + 2x^2 + 4x^3 + \cdots$$
  3. $$1 + x + 3x^2 + 9x^3 + \cdots$$
  4. $$1 + x + 4x^2 + 16x^3 + \cdots$$
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